Prasanna

By going through these CBSE Class 12 Hindi Notes Chapter 4 कैमरे में बंद अपाहिज Summary, Notes, students can recall all the concepts quickly.

कैमरे में बंद अपाहिज Summary Notes Class 12 Hindi Aroh Chapter 4

कैमरे में बंद अपाहिज कविता का सारांश

कैमरे में बंद अपाहिज कविता रघुवीर सहाय के काव्य-संग्रह ‘लोग भूल गए हैं से संकलित की गई है। इस कविता में कवि ने शारीरिक चुनौती को झेलते व्यक्ति से टेलीविजन कैमरे के सामने किस तरह के सवाल पूछे जाएंगे और कार्यक्रम को सफल बनाने के लिए उससे कैसी भंगिमा की अपेक्षा की जाएगी इसका लगभग सपाट तरीके से बयान करते हुए एक तरह से पीड़ा के साथ दृश्य संचारमाध्यम के संबध को रेखांकित किया है।

साथ ही कवि ने व्यंजना के माध्यम से ऐसे व्यक्ति की ओर इशारा किया है जो अपनी दुःख-दर्द, यातनावेदना को बेचना चाहता है। इस कविता में कवि ने शारीरिक चुनौती झेलते हुए लोगों के प्रति संवेदनशीलता व्यक्त की है। कवि ने इस कविता में बताया है कि अपने कार्यक्रम को सफल बनाने तथा किसी की पीड़ा को बहुत बड़े दर्शक वर्ग तक पहुँचाने के लिए दरदर्शनवाले किसी दल और शारीरिक रूप से कमजोर व्यक्ति को अपने कैमरे के सामने प्रस्तुत करते हैं। उससे अनेक तरह से सवाल पर सवाल पूछते हैं। उसे कैमरे के आगे बार-बार लाया जाता है। बार-बार उससे अपाहिज होने के बारे में सवाल पूछे जाते हैं

कि आपको अपाहिज होकर कैसा लगता है तथा उस कार्यक्रम को रोचक बनाने के लिए दूरसंचारवाले स्वयं प्रतिक्रिया व्यक्त करके बताते स हैं। अनेक ऐसे संवेदनशील सवालों को पूछ-पूछकर वे उस व्यक्ति को रुला देते हैं। दूरदर्शन के बड़े परदे पर उस व्यक्ति की आँसूभरी ” आँखों को दिखाया जाता है। इस प्रकार दूरदर्शनवाले बार-बार एक ऐसे अपाहिज व्यक्ति की पीड़ा को दर्शकों के समक्ष प्रस्तुत करते हैं।

कैमरे में बंद अपाहिज कवि परिचय

कवि-परिचय जीवन-परिचय-रघुवीर सहाय समकालीन हिंदी कविता के संवेदनशील कवि हैं। उनका जन्म सन् 1929 ई० में उत्तर प्रदेश के लखनऊ में हुआ था। उन्होंने लखनऊ विश्वविद्यालय से 1951 में एम० ए० अंग्रेजी की परीक्षा उत्तीर्ण की। एम० ए० करने के पश्चात ये पत्रकारिता क्षेत्र में कार्य करने लगे। इन्होंने ‘प्रतीक’, ‘वाक् और ‘कल्पना’ अनेक पत्रिकाओं के संपादक मंडल के सदस्य के रूप में भी कार्य किया।

ततपश्चात कुछ समय तक आकाशवाणी में ऑल इंडिया रेडियो के हिंदी समाचार विभाग से भी सबद्ध रहे। ये 1971 से 1982 तक प्रसिद्ध पत्रिका दिनमान के संपादक रहे। इनको कवि के रूप में ‘दूसरा सप्तक’ से विशेष ख्याति प्राप्त हुई। इनकी साहित्य सेवा भावना के कारण ही इनको साहित्य अकादमी सम्मान से सम्मानित किया गया। अंत में दिल्ली में सन् 1990 ई० में ये अपना महान साहित्य संसार को सौंपकर चिरनिद्रा में लीन हो गए।

रचनाएँ-रघुवीर सहाय हिंदी साहित्य के सफल कवि हैं। इन्होंने समकालीन समाज पर अपनी लेखनी चलाई है। इन्होंने समकालीन अमानवीय दोषपूर्ण राजनीति पर व्यंग्योक्ति तथा नए ढंग की कविता का आविष्कार किया है। इनकी प्रमुख रचनाएँ निम्नलिखित हैं

काव्य-संग्रह-सीढ़ियों पर धूप में, आत्महत्या के विरुद्ध, हँसो, हँसो जल्दी हँसो, लोग भूल गए हैं, आत्महत्या के विरुद्ध इनका प्रसिद्ध काव्य-संग्रह है। सीढ़ियों पर धूप में ‘कविता-कहानी-निबंध’ का अनूठा संकलन है। काव्यगत विशेषताएँ-रघुवीर सहाय समकालीन हिंदी जगत के प्रसिद्ध कवि हैं। उनका काव्य समकालीन जगत का यथार्थ चित्रण प्रस्तुत करता है। उनके काव्य की प्रमुख विशेषताएँ निम्नलिखित हैं

(i) समाज का यथार्थ चित्रण-रघुवीर सहाय जी ने समकालीन समाज का यथार्थ चित्रण प्रस्तुत किया है। इनके काव्य में सामाजिक यथार्थ के प्रति विशिष्ट सजगता दृष्टिगोचर होती है। इन्होंने सामाजिक अव्यवस्था, शोषण, विडंबना आदि का यथार्थ चित्रण किया है।

(ii) अदम्य जिजीविषा का चित्रण-रघुवीर सहाय ने अपने काव्य में अदम्य जिजीविषा का वर्णन किया है। इन की अनेक कविताओं में इस विशेषता का अनूठा चित्रण हुआ है। ‘सीढ़ियों पर धूप में’ काव्य-संग्रह की प्रायः सब कविताओं में अदम्य जीने की इच्छा। की सफल अभिव्यक्ति हुई है।

“और जिंदगी के अंतिम दिनों में काम करते हुए बाप काँपती साइकिलों पर
भीड़ से रास्ता निकाल कर ले जाते हैं।
तब मेरी देखती हुई आँखें प्रार्थना करती हैं
और जब वापस आती हैं अपने शरीर में
तब दे दिया जा चुका होता है।”

(iii) मध्यवर्गीय जीवन का चित्रण-कवि ने समकालीन समाज के मध्यवर्गीय जीवन का यथार्थ चित्रांकन प्रस्तुत किया है। इन्होंने अपने काव्य में मध्यवर्गीय जीवन में परिव्याप्त तनावों और विडंबनाओं का वर्णन किया है। वह कवि और शेष दुनिया के बीच का अनुभूत तनाव है। जो कवि को निरंतर आंदोलित करता रहता है। इसके साथ-साथ कवि ने कुछ व्यक्ति और समूह के मध्य तनाव का चित्रांकन भी किया है।

(iv) भ्रष्टाचार का चित्रण-रघुवीर सहाय ने अपने काव्य में समकालीन समाज में फैले भ्रष्टाचार का यथार्थ चित्रण किया है। इन्होंने लोकतंत्र में व्याप्त भ्रष्टाचार की प्रत्येक गतिविधि का मार्मिक वर्णन किया है। ‘आत्महत्या के विरुद्ध’ एक नाटकीय एकालाप है | जिसमें भ्रष्टाचार को ध्वन्यात्मक रूप से अंकित किया गया है। इस संग्रह में कवि ने ‘समय आ गया है’ वाक्यांश के माध्यम से

By going through these CBSE Class 12 Physics Notes Chapter 11 Dual Nature of Radiation and Matter, students can recall all the concepts quickly.

Dual Nature of Radiation and Matter Notes Class 12 Physics Chapter 11

→ Radiation has dual nature i.e., it behaves both as a particle and a wave.

→ Energy greater than work function (Φ₀ or ω) required for ejection of electrons from the metal surface can be supplied by heating or irradiating it by the light of frequency greater than threshold frequency or applying a strong electric field.

→ The stopping potential (V₀) depends on the frequency of incident light, nature of the material on the surface of the cathode.

→ V₀ is directly related to the maximum kinetic energy (\(\frac{1}{2}\) mV²_max) of the emitted electrons i.e., eV₀ = E_max = \(\frac{1}{2}\) m V²_max).

→ V₀ is independent of the intensity of incident light for a given frequency.

→ Below the threshold frequency (v₀), no photoelectric emission takes place whatever may be its intensity.

→ Photoelectric emission is an instantaneous process.

→ The photoelectric current depends on the potential difference applied between the cathode and anode, the nature of the material of the cathode, and the intensity of incident light.

→ The photoelectric emission follows the law of conservation of energy.

→ Each photon absorbed ejects an electron from a metal surface. Einstein’s photoelectric equation is in accordance with the law of conservation of energy.

→ The dualism of matter is inherent in the de-Broglie relation which contains a wave concept (λ) and a particle concept (p).

→ The de-Broglie wavelength (λ) associated with a moving particle is related to its momentum (p) as
λ = \(\frac{h}{p}\)

→ The de-Broglie wavelength is independent of the charge and nature of the material particle.

→ The wave nature of electrons has been verified and confirmed using Davisson and Germer’s experiments.

→ Free electrons in a metal are free in the sense that they move inside the metal in a constant potential.

→ Plank’s constant is the bridge between the particle aspect and wave aspect of radiation and matter.

→ The wave-particle duality is not the sole monopoly of e.m. waves.

→ Even a material particle in motion according to de-Broglie will have a wavelength.

→ The photoelectric effect was discovered by Hertz in 1887.

→ The photoelectric effect was demonstrated by Hallwach in 1888.

→ Work function is least for Caesium (i.e Φ₀ = 2.14 eV)

→ Absorption of energy takes place in discrete units of hv.

→ Platinum has the highest value of work function.

→ Zn, Cd, Mg, etc. respond only to UV light (having a short wavelength) to cause electron emission from the surface.

→ Alkali metals such as Li, Na, K, Caesium, and rubidium are sensitive even to visible light.

→ The number of photoelectrons emitted per second is directly proportional to the intensity of incident radiation.

→ Work function: It is defined as the minimum energy required by an electron to come out from a metal surface.

→ Photo electrons: The electrons ejected out of a metal surface under the action of light of a short wavelength are called photoelectrons.

→ Photoelectric effect: It is defined as the phenomenon of ejection of electrons from a metal surface when the light of very high frequency falls upon it.

→ Photon: It is a packet of energy.

→ Photoelectric cell: ft is a device that converts light energy into electrical energy.

→ Matter waves or de-Broglie waves: They are defined as the waves associated with every moving matter particle.

→ Cutoff potential or Retarding potential or stopping potential: It is defined as the minimum value of negative potential which has to be applied on the anode in a photocell so that the photoelectric current becomes zero. It is denoted by V₀.

→ Saturation Current: It is the maximum value of the photoelectric current.

Important Formulae
→ For a relativistic particle moving with a speed v comparable to the speed of light c, de-Broglie wavelength is given by
λ = \(\frac{h}{m v}\)
where m = \(\frac{m_{0}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}\), m₀ being the rest mass of the particle.

→ deBroglie wavelength of a particle is
λ = \(\frac{\mathrm{h}}{\mathrm{p}}=\frac{\mathrm{h}}{\mathrm{m} v}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mE}}}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{meV}}}\)
where p = momentum of particle of mass m, its velocity = v
E = K.E. of particle.
V = accelerating potential difference applied (V).

→ For an electron,
λ = \(\frac{12.27}{\sqrt{V}}\) A°
where \(\frac{\mathrm{h}}{\sqrt{2 \mathrm{me}}}\) = 12.27 × 10^-10 for an electron

→ Vertical deflection of electron due to \(\overrightarrow{\mathrm{E}}\) between its plates is
y = \(\frac{1}{2}\) at2 = \(\frac{1}{2}\) . \(\frac{\mathrm{e} \mathrm{E}}{\mathrm{m}} \cdot \frac{\mathrm{x}^{2}}{v^{2}}\)

→ Total deflection of the charge on the screen is
y₀ = \(\frac{\mathrm{eEx}}{\mathrm{m} v^{2}}\left(1+\frac{\mathrm{x}}{2}\right)=\left(1+\frac{\mathrm{x}}{2}\right)\) tan θ
where l = distance of screen from the end of plates.
x = length of plates
tan θ = \(\frac{v_{\mathrm{y}}}{v_{x}}=\frac{y_{0}}{\left(l+\frac{x}{2}\right)}\)

→ Einstein’s photoelectric equation is
hv = hv₀ + \(\frac{1}{2}\) m v²_max
or
\(\frac{hv}{λ}\) = W + eV₀, where the symbols have their usual meanings.

→ At the threshold frequency v^ the emitted phtoelectrons will have no K.E.
∴ 0 = hv₀ – ω
or
ω = hv₀.

→ At stopping potential, \(\frac{1}{2}\) m v2 max = eV₀.

→ Be v max = \(\frac{m v_{\max }^{2}}{r}\)

→ p = \(\frac{hv}{C}\) = momentum of a photon

→ Slope of V – ν curve = \(\frac{\mathrm{V}}{\mathrm{ν}}=\frac{\mathrm{h}}{\mathrm{e}}\)

→ Number of photons per sec per unit area = \(\frac{Φ}{E}\)
= \(\frac{\text { energy flux }}{\text { energy of photons per sec per unit area }}\)

= \(\frac{\text { Energy radiated/sec }}{\text { Energy of each photon }}=\frac{\mathrm{P}}{\mathrm{E}}\)

By going through these CBSE Class 12 Physics Notes Chapter 10 Wave Optics, students can recall all the concepts quickly.

Wave Optics Notes Class 12 Physics Chapter 10

→ Optics is that branch of physics that deals with the nature, sources, properties and effects of light.

→ Light is that form of energy that makes the object visible.

→ Wave optics treat the light as e.m. waves.

→ Light does not require any material medium for propagation.

→ Photographic plates are sensitive to the violet colour and least sensitive to the red colour.

→ Angular fringe width i.e., θ is independent of the distance between the screen and the plane of the slits i.e., D.

→ Speed of light is maximum for violet colour (7.5 × 10¹⁴ Hz) and minimum for red colour (4.3 × 10¹⁴ Hz).

→ Objects are visible from all directions due to the scattering of light.

→ The velocity of light of all wavelengths is the same in free space or vacuum.

→ Hie velocity of light of different colours will be different in media other than vacuum.

→ Our eye fails to see two points separately if they subtend an angle equal to or less than 1 minute and it is called resolving power of the eye.

→ Light of single frequency is called monochromatic.

→ The wavefront due to a point source is spherical and due to a line source, it is cylindrical.

→ The wavefront corresponding to a parallel beam of a light ray is plane.

→ The direction of propagation of light is perpendicular to the wavefront.

→ Each point on a wave point acts as a source of new disturbance and is called a secondary wavelet.

→ Polaroids allow the light oscillations parallel to the transmission axis to pass through them.

→ If the transmission axis of the analyser is perpendicular to that of the polariser, then no light passes through the analyser.

→ If the transmission axis of the polarizer and analyser are parallel, then the whole of the polarised light passes through the analyser.

→ The optical axis is the plane in a polariser or analyser parallel to which the oscillations of light are transmitted through the crystal without change in intensity.

→ Sound waves in the air cannot be polarised as they are longitudinal waves.

→ The tire angle between the direction of propagation and the plane of polarisation or plane of oscillation is 0°.

→ The angle between the direction of oscillation and the direction of propagation is 90°

→ The polarization of light is determined by the change in \(\overrightarrow{\mathrm{E}}\) field vector only.

→ The light is polarised in the plane of incidence by reflection.

→ In the interference, the energy is not destroyed but is redistributed.

→ The sustained interference is obtained by using coherent sources.

→ The order of the central maximum in the interference pattern is zero (i.e., n = 0).

→ When a transparent sheet or film of thickness t is introduced in the path of a ray of light from one slit, the interference pattern is shifted to the same side and an additional path difference of (μ – 1) t is introduced.

→ The interference occurs due to the superposition of wavelets from two wavefronts and the diffraction occurs due to the superposition of wavelets from two parts of the same wavefront.

→ The degree of diffraction is higher for longer wavelengths and thus greater is the deviation of the light waves from the rectilinear path.

→ Due to a lower degree of diffraction, the light waves appear to be travelling in straight lines.

→ The intensity of diffraction fringes decreases as the order of the maximum increases.

→ All interference fringes are of the same intensity

→ Coherent sources can be obtained by reflection, refraction or by the partial reflection of light.

→ Central fringe is always white surrounded by some coloured fringes when monochromatic light is replaced by white light

→ Wavefront: It is defined as the locus of all the particles of a medium vibrating in the same phase,

→ Unpolarised light: It is the light having electric field oscillations in all directions perpendicular to the direction of propagation,

→ Polaroids: They are defined as thin films of ultramicroscopic crystals of quinine idosulphate (called herpathite) with their optic axis parallel to each other.

→ Polarisers: They are defined as the crystals or polaroids on which unpolarised light is incident.

→ Analysers: They are defined as the crystals on which polarised light is incident.

→ Diffraction is the phenomenon of bending waves around the comers of the obstacles or apertures.

→ The resolving power of an optical instrument is its ability to show two closely placed point objects as just separate.

→ Limit of resolution: It is defined as the reciprocal of the resolving power.

→ Fringe Width: It is defined as the spacing between any two consecutive dark or bright fringes. It is denoted by β.

Important Formulae and Laws

→ Doppler’s shift for light is given by :
Δλ = ± \(\frac{λ}{c}\) u
where u is the speed of the source or the observer,
c is the speed of light,
λ is the original wavelength.

→ Malus law:
I = I₀ cos² θ.
where I0 is the intensity of the polarised light incident on the analyser.
θ = angle between the transmission axes of the polariser and analyser.

→ I = \(\frac{\mathrm{I}_{\mathrm{i}}}{2}\) cos² θ
where I_i is the intensity of the unpolarised light incident on the polariser and
I = intensity of the light transmitted through the analyser.
and I₀ = \(\frac{\mathrm{I}_{\mathrm{i}}}{2}\)

→ Polarisation by reflection is given by
μ = tan i_p.
where i_p is the Brewster’s angle

→ Phase difference and path difference (Δx) are related as:
ΔΦ = \(\frac{2 \pi}{\lambda}\) Δx

→ \(\frac{I_{\max }}{I_{\min }}=\frac{\left(a_{1}+a_{2}\right)^{2}}{\left(a_{1}-a_{2}\right)^{2}}\)

→ The fringe width is given by
β = \(\frac{\lambda \mathrm{D}}{\mathrm{d}}\)

→ The location of nth bright fringe on the screen is given by
y_n = nβ = n\(\frac{\lambda \mathrm{D}}{\mathrm{d}}\)

→ The distance of nth dark fringe is given by
y_n = (2n – 1)\(\frac{\lambda}{2 \mathrm{~d}}\)

→ The angular, separation for
1. nth bright fringe is given by
θ_n = \(\frac{\mathrm{n} \beta}{\mathrm{D}}=\frac{\mathrm{n} \lambda}{\mathrm{d}}\)

2. for nth dark fringe :
θn = (2n – 1)\(\frac{\lambda}{2 d}\)

→ Path difference for maximum of interference pattern is :
Δx = 2n\(\frac{λ}{2}\)

→ Path difference for minimum of interference pattern is :
Δx = \(\frac{(2 n+1) \lambda}{2}\)

→ Limit of resolution of telescope is given by
θ = \(\frac{1.22 \lambda}{\mathrm{d}}\)
where d = diameter of the aperture of the objective.

→ The number of fringes and wavelength of light used are related as
n₁λ₁ = n₂λ₂

→ Slit width and intensity are related as
\(\frac{\mathrm{W}_{1}}{\mathrm{~W}_{2}}=\frac{\mathrm{I}_{1}}{\mathrm{I}_{2}}\)

→ The amplitude of light wave and the slit width are related as :
\(\frac{\mathrm{I}_{1}}{\mathrm{I}_{2}}=\frac{\mathrm{A}_{1}^{2}}{\mathrm{~A}_{2}^{2}}=\frac{\mathrm{W}_{1}}{\mathrm{~W}_{2}}\)
or
\(\frac{W_{1}}{W_{2}}=\left(\frac{A_{1}}{A_{2}}\right)^{2}\)

→ Wavelength in a medium is given by
λ’ = \(\frac{λ}{μ}\)

→ Fringe width in the medium of R.I. p is given by
β’ = \(\frac{\lambda^{\prime} D}{d}=\frac{\lambda D}{\mu d}\)

→ Width of central diffraction maximum, β0 = \(\frac{2 \lambda \mathrm{D}}{\mathrm{d}}\)

→ HaLf angular width of central maximum,
θ₁ = \(\frac{λ}{a}\)

→ Fresnel distance,
Z_f = \(\frac{a^{2}}{\lambda}\)

→ R.P. of microscope = 2 \(\frac{\mu \sin \theta}{\lambda}\)

→ Angular limit of resolution of telescope, dθ = \(\frac{1.22 \lambda}{\mathrm{D}}\)

→ Angular position of nth secondary minimum,
θ_n = \(\frac{nλ}{a}\)

→ Distance of nth secondary maximum from centre of screen,
y_n = \(\frac{\mathrm{n} \lambda \mathrm{D}}{\mathrm{a}}\)
where a = slit width.

 

By going through these CBSE Class 12 Hindi Notes Chapter 3 कविता के बहाने, बात सीधी थी पर Summary, Notes, students can recall all the concepts quickly.

कविता के बहाने, बात सीधी थी पर Summary Notes Class 12 Hindi Aroh Chapter 3

कविता के बहाने, बात सीधी थी पर कविता का सारांश

श्री कुँवर नारायण की इस कविता की रचनात्मकता और उसमें छिपी अपार ऊर्जा को प्रतिपादित करने में सक्षम है। कविता के लिए शब्दों : । का संबंध सारे जड़-चेतन से है। यह अतीत, वर्तमान और भविष्य से जुड़ी हुई है। इसकी व्यापकता अपार है। इसकी कोई सीमा नहीं है। । यह किसी प्रकार के बंधन में बँधती नहीं। इसके लिए न तो भाषा का कोई बंधन है और न ही समय का। ‘कविता के बहाने’ नामक कविता | आकार में छोटी है पर भाव में बहुत बड़ी है। आज का समय मशीनीकरण और यांत्रिकता का है जिसमें सर्वत्र भाग-दौड़ है। मनुष्य का मन :

इस बात से आशंकित रहता है कि क्या कविता रहेगी या मिट जाएगी। क्या कविता अस्तित्वहीन हो जाएगी ? कवि ने इसे एक यात्रा माना। – है जो चिड़िया, फूल से लेकर बच्चे तक है। चिड़िया की उड़ान सीमित है, पर कविता की उड़ान तो असीमित है। भला चिड़िया की उड़ान ।

कविता जैसी कैसे हो सकती है। कविता के पंख तो सब जगह उसे ले जा सकते हैं पर चिड़िया के पंखों में ऐसा बल कहाँ है! कविता :
का खिलना फल के खिलने का बहाना तो हो सकता है पर फल का खिलना कविता जैसा नहीं हो सकता। फ – कुछ ही देर बाद मुरझा जाता है लेकिन कविता तो भावों की महक लेकर बिना मुरझाए सदैव प्रभाव डालती रहती है। कविता तो बच्चों के – खेल के समान है जिसकी कोई सीमा ही नहीं है। जैसे बच्चों के सपनों की कोई सीमा नहीं, वे भविष्य की ओर उड़ान भरते हैं वैसे ही कविता भी शब्दों का ऐसा अनूठा खेल है जिस पर किसी का कोई बंधन नहीं है। कविता का क्षेत्र सीमा-रहित है। वह किसी भी सीमा से – पार निकली हुई राह में आने वाले सभी बंधनों को तोड़ कर आगे बढ़ जाती है।

बात सीधी थी पर कविता का सारांश

‘बात सीधी थी पर’ कविता में कुँवर नारायण ने यह स्पष्ट किया है कि जब भी कवि कोई रचना करने लगता है तो उसे अपनी बात को सहज भाव से कह देना चाहिए, न कि तर्क-जाल में उलझाकर अपनी बात को उलझा देना चाहिए। आडंबरपूर्ण शब्दावली से युक्त रचना कभी भी प्रभावशील तथा प्रशंसनीय नहीं होती। इसके लिए कवि ने पेंच का उदाहरण दिया है।

पेंच को यदि सहजता से पेचकस से कसा जाए वह कस जाती है। यदि उसके साथ जबरदस्ती की जाए तो उसकी चूड़ियाँ घिस कर मर जाती हैं और उसे ठोंककर वहीं दबाना पड़ता है। इसी प्रकार से अपनी अभिव्यक्ति में यदि कवि सहज भाषा का प्रयोग नहीं करता तो उसकी रचना प्रभावोत्पादक नहीं बन पाती। सही बात को सही शब्दों के माध्यम से कहने से ही रचना प्रभावशाली बनती है।

कविता के बहाने, बात सीधी थी पर कवि परिचय

कवि-परिचय जीवन-परिचय-कुँवर नारायण आधुनिक हिंदी साहित्य में नई कविता के प्रमुख कवि माने जाते हैं। इनका अज्ञेय के तारसप्तक’ में महत्वपूर्ण स्थान है। इनका जन्म उत्तर प्रदेश के फैजाबाद जिले में 19 सितंबर, 0 1927 को हुआ था। इनकी प्रारंभिक शिक्षा स्थानीय स्कूल में हुई। इन्होंने लखनऊ विश्वविद्यालय से उच्च o शिक्षा ग्रहण की। कुछ दिनों तक ‘युग चेतना’ नामक प्रसिद्ध साहित्यिक मासिक पत्रिका का संपादन किया।

ये एक भ्रमणशील व्यक्ति थे। इन्होंने चेकोस्लोवाकिया, पोलैंड, रूस, चीन आदि देशों का भ्रमण किया। रचनाएँ- श्री कुँवर नारायण अज्ञेय द्वारा संपादित तीसरे सप्तक के प्रमुख कवि हैं। ये बहुमुखी प्रतिभा के धनी साहित्यकार हैं। इन्होंने साहित्य की अनेक विधाओं पर सफल लेखनी चलाई है, लेकिन एक कवि रूप में अधिक प्रसिद्ध हुए हैं। इनकी प्रमुख रचनाएँ निम्नलिखित हैं
(i) काव्य-संग्रह-चक्रव्यूह (1956), परिवेश : हम-तुम, अपने सामने, कोई दूसरा नहीं, इन दिनों आदि।
(ii) प्रबंध काव्य-आत्मजयी।
(iii) कहानी संग्रह-आकारों के आस-पास।
(iv) समीक्षा-आज और आज से पहले।
(v) साक्षात्कार-मेरे साक्षात्कार।

साहित्यिक विशेषताएँ-
कुँवर नारायण का काव्य संबंधी दृष्टिकोण अत्यंत उच्च एवं श्रेष्ठ है। तीसरे सप्तक में कुँवर नारायण ने जो वक्तव्य ० दिया है उसके आधार पर उनकी भव्य-दृष्टि को बखूबी समझा जा सकता है। उनकी काव्य-चेतना अत्यंत उत्तम है। उनके साहित्य की प्रमुख विशेषताएँ निम्नलिखित हैं

(i) वैज्ञानिक दृष्टिकोण-कुँवर नारायण एक भ्रमणशील व्यक्ति हैं। उनकी इसी भ्रमणशीलता तथा पाश्चात्य साहित्य के अध्ययन के फलस्वरूप कविता के प्रति इनका वैज्ञानिक दृष्टिकोण है। उन्होंने अपने काव्य में वैज्ञानिक दृष्टिकोण को प्रमुखता प्रदान की है। उन्होंने वैज्ञानिक दृष्टिकोण को स्पष्ट करते हुए कहा है कि ‘यह वह दृष्टि है जो सहिष्णु और उदार मनोवृत्ति से जुड़ी हुई है। वैज्ञानिक दृष्टि जीवन को किसी पूर्वाग्रह से पंगु करके नहीं देखती, बल्कि उसके प्रति एक बहुमुखी सतर्कता बरतती है।’

(ii) विचार पक्ष की प्रधानता-कुँवर नारायण का साहित्य जहाँ एक ओर वैज्ञानिक दृष्टिकोण से ओत-प्रोत है, वहीं दूसरी ओर उसमें विचार पक्ष की भी प्रधानता है। इसी प्रधानता के कारण वे कविता को कोरी भावुकता का पर्याय नहीं मानते। उन्होंने अपने काव्य में विचारों को अधिक महत्व दिया है, उसके बाह्य आकर्षण पर नहीं। यही कारण है कि इनकी कविता गंभीरता लिए हुए हैं।

(iii) प्रतीकात्मकता-कवि ने अपनी संवेदना को अभिव्यक्त करने के लिए प्रतीकात्मकता का सहारा लिया है। उनका चक्रव्यूह काव्यसंग्रह एक प्रतीकात्मक रचना है जिसमें कवि ने समकालीन समस्याओं में डूबे मानव को विघटनकारी सात महारथियों से घिरे हुए अभिमन्यु के रूप में चित्रित किया है।

(iv) नगरीय संवेदना का चित्रण-कुँवर नारायण को नगरीय संवेदना का कवि माना जाता है। यह पक्ष उनके काव्य में स्पष्ट झलकता है। उन्होंने नगर तथा महानगरीय सभ्यता का अपने काव्य में यथार्थ चित्रण किया है।

(v) सामाजिक चित्रण-कुँवर नारायण जी सामाजिक चेतना से ओत-प्रोत कवि हैं। उन्होंने अपनी रचनाओं में समकालीन समाज की। यथार्थ झाँकी प्रस्तुत की है। ‘आत्मजयी’ प्रबंध काव्य में नचिकेता के मिथक के माध्यम से उन्होंने सामाजिक जीवन का सजीव चित्रांकन किया है। सामाजिक रहन-सहन, उहापोह आदि का इनके काव्य में यथार्थ चित्रण हुआ है।

(vi) मानवतावाद-कुँवर नारायण के काव्य में मानवतावादी विराट भावना के दर्शन भी होते हैं। उन्होंने वैज्ञानिक युग की भागदौड़ में फँसे सामान्य जन-जीवन का चित्रण किया है। ‘चक्रव्यूह’ काव्य संग्रह में कवि ने समकालीन मानव को विघटनकारी सात-सात महारथियों से घिरे हुए अभिमन्यु के रूप में चित्रित किया है।

(vii) भाषा-शैली-भाषा और विषय की विविधता कुँवर नारायण की कविताओं के विशेष गुण हैं। उन्होंने विषय-विविधता के साथ साथ अनेक भाषाओं का प्रयोग भी किया है। उनके काव्य की प्रमुख भाषा साहित्यिक खड़ी बोली है जिसमें अंग्रेजी, उर्दू, फ़ारसी, तत्सम और तद्भव शब्दावली का प्रयोग है। उनकी शैली विषयानुरूप है जो अत्यंत गंभीर, विचारात्मक तथा प्रतीकात्मक है।

(viii) अलंकार-कुँवर जी के साहित्य में विचारों की प्रधानता है इसलिए सौंदर्य की ओर इनका ध्यान कम ही गया है। इनके काव्य में अलंकारों का स्वाभाविक प्रयोग हुआ है। अनुप्रास, यमक, उपमा, पदमैत्री, स्वरमैत्री, रूपक आदि अलंकारों का प्रयोग हुआ है। . मुक्तक छंद का प्रयोग है। बिंब योजना अत्यंत सुंदर एवं सटीक है। निष्कर्ष रूप में हम कह सकते हैं कि कुँवर नारायण आधुनिक हिंदी साहित्य के प्रमुख कवि हैं। उनका साहित्यिक दृष्टिकोण अत्यंत वैज्ञानिक है, अतः उनका आधुनिक काव्यधारा में प्रमुख स्थान है।

 

By going through these CBSE Class 12 Physics Notes Chapter 9 Ray Optics and Optical Instruments, students can recall all the concepts quickly.

Ray Optics and Optical Instruments Notes Class 12 Physics Chapter 9

→ The image formed by a concave mirror cannot lie beyond the focus.

→ Real images are always inverted.

→ Virtual images are always erect.

→ The minimum distance between an object and its real image formed by a concave mirror is zero.

→ The angle of deviation on refraction of light from a plane surface is given by δ = |i – r|.

→ The absolute R.I. of any medium is always greater than one.

→ The frequency of light does not change during the refraction of light.

→ When light travels from rarer to denser medium its wavelength decreases as λ_m = \(\frac{\lambda}{\mu}\) and μ > 1, so λ_m < λ. where λ_m is the wavelength of light in the denser medium.

→ If the critical angle for water is C, then the fish just below the surface of the water can see in an angular range of 2C.

→ When i = r = 0, then refraction takes place without a change in the path of the ray of light.

→ The value of the refractive index depends on the following:
(a) Nature of the media of incidence and refraction.
(b) Temperature of media.
(c) Colour of light or wavelength of light.

→ ‘μ’ decreases with the increase in temperature.

→ μ is independent of the angle of incidence.

→ The transmission involves two refractions.

→ The maximum value of μ is for diamond (μ = 2.46).

→ The critical angle for the red rays is more than that for blue rays.

→ The critical angle increases with temperature.

→ Critical angle depends on the refractive index, the colour of light and temperature of the medium.

→ Air bubbles in glass appear silvery-white due to the total internal reflection from them.

→ Critical angles for water-air, glass-air and diamond-air are 45° 42° and 24° respectively.

→ The critical angle for ordinary glass is 42°

→ Thicker is the lens, more is the bending of light rays, thus lesser is its focal length and hence more is the power of the lens and vice-versa for a thin lens i.e., the thin lens has less power and longer focal length.

→ To produce dispersion without deviation, the angle of crown glass prism has to be greater than that of flint glass prism i.e., A > A’ and (μ’ – 1) > (μ’ – 1).

→ For no dispersion, the materials and the angles of the two prisms should be chosen so that their dispersive powers are in the inverse ratio of the deviations suffered by mean light through the prism. To produce deviation without dispersion, the angle of the crown glass prism has to be greater than that of the flint glass prism.

→ As μv, μr and μ are constant for a given material, so dispersive power (ω) of given material of a prism cannot be changed. But if glass material is chosen in such a way that μv is greater and μr is lower, then co can be higher.

→ A single lens cannot be free from chromatic aberration as it has different focal length for different colours and thus they are focused at different points.

→ To compare the size of the two objects, they should be placed at the least distance of distinct vision i.e. D = 25 cm.

→ The magnifying power of the simple microscope is small.

→ For greater magnification, a compound microscope is used which has net magnifying power as the product of linear magnifications or magnifying powers of each lens.

→ The image formed by the simple microscope is erect and magnified while the image formed by the compound microscope is inverted.

→ A simple microscope is also called a reading lens and is also used for repair of small instruments while compound microscope cannot be used for these purposes.

→ Magnifying power of an astronomical telescope is greater in case of the image formed at the least distance of distinct vision than in case of normal adjustment i.e, \(\frac{\mathrm{f}_{0}}{\mathrm{f}_{\mathrm{e}}}\)(1 + \(\frac{\mathrm{f}_{\mathrm{e}}}{\mathrm{D}}\)) > \(\frac{\mathrm{f}_{0}}{\mathrm{f}_{\mathrm{e}}}\)

→ The skin becomes visible before the actual sunrise and remains visible after actual sunset due to refraction. It increases the length of the day by nearly 4 minutes.

→ The image of an object when seen through a slab of thickness and R.I. μ is shifted by a distance, d = t(1 – \(\frac{1}{\mu}\))

→ When the object is in a denser medium, then its apparent depth is lesser than the actual depth if observed from the rarer medium.

→ When the object is in a rarer medium, then its apparent depth is greater than the actual depth if observed from the denser medium. The focal length of a lens immersed in water becomes four times the focal length in air.

→ Rainbow is seen only by a person with his back facing the sun and his eyes make an angle of 42° with the axis of the rainbow.

→ The nature of the lens does not change if it is placed in a rarer medium i.e.,μ_g > μ_med but the focal length in the medium becomes more than that in air i.e. f_m > f_a.

→ If μ_m > μ_g i.e. if it is placed in a denser medium, then the nature of the lens changes. Tire focal length may increase or decrease depending on the value of \(\frac{\mu_{g}-\mu_{m}}{\mu_{m}}\) as compared to (μ_g – 1).

→ f_m increases if \(\frac{\mu_{\mathrm{g}}-\mu_{\mathrm{m}}}{\mu_{\mathrm{m}}}\) > (μ_g – 1)

→ f_m decreases if \(\frac{\mu_{\mathrm{g}}-\mu_{\mathrm{m}}}{\mu_{\mathrm{m}}}\) < (μ_g – 1)

→ f_m = f_a, if \(\frac{\mu_{\mathrm{g}}-\mu_{\mathrm{m}}}{\mu_{\mathrm{m}}}\) = (μ_g – 1)

→ The lens becomes invisible if μ_m = μ_g and behaves as a plain glass with no refraction.

→ Amplitude, intensity, velocity and wavelength of the wave change on refraction.

→ In a denser medium, refraction does not occur when the angle of incidence is greater than the critical angle.

→ Rainbow is caused by the combined effect of refraction, total internal reflection and dispersion of sunlight by the raindrops suspended in the air.

→ Black is not the colour of light. It shows the absence of light.

→ White is also not the colour of light. It depicts the presence of all the colours.

→ Blue, green and red is primary colours.

→ Our eye is not sensitive to UV and infrared light.

→ Tire final image formed by the reflecting telescope is free from chromatic aberration. Also, the brightness of the image formed is higher.

→ The far point of the normal eye is at infinity.

→ Far Point: The farthest point up to which the eye can see clearly is called the far point.

→ Least distance of distinct vision: It is defined as the distance at which the eye can see the objects clearly. For a normal eye, it is 25 cm.

→ Small deviation produced by a prism is independent of the angle of incidence.

→ A pure spectrum is defined as that spectrum in which there is no missing constituent colour.

→ An impure spectrum is one in which there is overlapping of almost all the colours so at the centre of the spectrum we obtain a white spot with edges coloured with red and violet.

→ Transmission: It is defined as the passing of a ray of light through the medium.

→ Optical path: It is the product of the refractive index of the medium (μ) and the distance covered in it (n).
i. e., optical path = μ_x = μ (geometrical path).

→ For refraction from rarer to denser medium, r < i.

→ Critical angle: It is defined as the angle of the incidence in the denser medium for which the angle of refraction is 90° in the rarer medium.

→ Dispersion: It is defined as the process of splitting up white light into its constituent colours on passing through the prism.

→ Cauchy’s Formula: It states that the R.I. of a material depends on the wavelength (λ) as:
μ = a + \(\frac{b}{\lambda^{2}}+\frac{c}{\lambda^{4}}\)

→ Spectrum: It is defined as the band of colours that are obtained due to the dispersion of light.

→ Rainbow: Beautiful colours seen in the sky when the sun shines after the rain.

→ Fraunhofer lines: They are defined as the large number of dark lines observed in the spectrum of sunlight which corresponds to the absorption spectrum.

→ Primary rainbow: It is the rainbow in which the violet and red rays make angles 410 and 43° respectively with the axis of the rainbow. The red colour lies at the top while violet at the bottom.

→ Secondary rainbow: It is the rainbow in which the violet and red colours make angles 54° and 51° respectively with its axis. It is less bright than a primary rainbow. The violet colour lies on the outer edge while red on the inner edge.

→ The primary rainbow is formed due to two refractions and one total internal reflection of light incident on the droplet while the secondary rainbow is formed due to two refractions and two total

→ internal reflections of the light incident on the droplets.

→ Angular dispersion: It is defined as the difference between the angles of deviation for the extreme colours.

→ Dispersive power: It is defined as the ratio of angular dispersion to the mean deviation.

→ Chromatic aberration: It is defined as the process due to which a lens forms images of different colours at different distances from the lens.

→ Chromatic aberration = f_r – f_v.

Important Formulae

→ μ = \(\frac{C}{v}=\frac{\sin \mathrm{i}}{\sin \mathrm{r}}\),
where i = angle of incidence,

→ ^aμ_w = \(\frac{\text { Real depth }}{\text { apparent depth }}\)

→ μ =\(\frac{1}{\sin C}\) when C = critical angle

→ ^wμ_g = \(\frac{{ }^{a} \mu_{g}}{{ }^{a} \mu_{w}}\)when ^wμ_g is the R.I. of glass w.r.t. water.

→ ^aμ_b = \(\frac{1}{{ }^{b} \mu_{a}}\)

→ Refraction formula when the refraction takes place at convex spherical surface from rarer to denser medium for real image of object is:
– \(\frac{\mu_{1}}{u}+\frac{\mu_{2}}{v}=\frac{\mu_{2}-\mu_{1}}{R}\)

→ For virtual image, it is again same.

→ When refraction takes place from denser to rarer medium; it is given by
– \(\frac{\mu_{2}}{u}+\frac{\mu_{1}}{v}=\frac{\mu_{1}-\mu_{2}}{R}\)

→ Lens formula is
– \(\frac{1}{\mathrm{u}}+\frac{1}{\mathrm{v}}=\frac{1}{\mathrm{f}}\)

→ Lens Maker’s formula is
\(\frac{1}{f}\) = (μ – 1)(\frac{1}{R_{1}}-\frac{1}{R_{2}})

→ Power of a lens is given by
P = \(\frac{1}{\mathrm{f}(\mathrm{m})}\) (Dioptre) or D

→ Linear magnification produced by a lens:
m = \(\frac{1}{\mathrm{O}}=\frac{v}{\mathrm{u}}=\frac{\mathrm{f}}{\mathrm{f}+\mathrm{u}}=\frac{\mathrm{f}-v}{\mathrm{f}}\)

→ Focal length of combination of two lenses placed in contact is
\(\frac{1}{\mathrm{~F}}=\frac{1}{\mathrm{f}_{1}}+\frac{1}{\mathrm{f}_{2}}\)

→ Power of combination is
P = P₁ + P₂

→ When the two lenses are placed at a distance ‘d’; then
\(\frac{1}{\mathrm{~F}}=\frac{1}{\mathrm{f}_{1}}+\frac{1}{\mathrm{f}_{2}}-\frac{\mathrm{d}}{\mathrm{f}_{1} \mathrm{f}_{2}}\)

→ Power of spherical refracting surface is
P = \(\frac{\mu_{2}-\mu_{1}}{R}\)

→ Lateral shift is given by
d = \(\frac{t}{\cos r}\) sin (i – r)

→ Magnification produced by lens combination is
m = m₁ × m₂

→ For a prism,

1. A = r₁ + r₂
2. μ = \(\frac{\sin \left(\mathrm{A}+\delta_{\mathrm{m}}\right) / 2}{\sin \frac{\mathrm{A}}{2}}\)
3. A + δ = i + e.
4. For small angled prism, δ = (μ – 1)A.

→ Dispersive power is
W = δ_v – δ_r /δ = \(\frac{\mu_{v}-\mu_{r}}{\mu-1}\)

→ Condition for no deviation:
\(\frac{\mathrm{A}^{\prime}}{\mathrm{A}}=-\frac{(\mu-1)}{(\mu-1)}\)
net angular dispersion = δ (ω – ω’)

→ Condition for no dispersion:
1. \(\frac{\mathrm{A}^{\prime}}{\mathrm{A}}=-\frac{\mu_{\mathrm{v}}-\mu_{\mathrm{r}}}{\mu_{\mathrm{v}}-\mu_{\mathrm{r}}}\)

2. \(\frac{\omega}{\omega^{\prime}}=-\frac{\delta^{\prime}}{\delta}\)
Net deviation = δ(1 – \(\frac{\omega}{\omega^{\prime}}\))

→ Chromatic aberration is
f_r – f_v = w × f

→ Magnifying power of simple microscope is given by:
m = \(\frac{\beta}{\alpha}\) = 1 + \(\frac{\mathrm{D}}{\mathrm{f}}\)

When image is formed at infinity, then M = \(\frac{\mathrm{D}}{\mathrm{f}}\)

→ For compound microscope
M = \(\frac{v_{0}}{u_{0}}\)(1 + \(\frac{D}{f_{e}}\)) = – \(\frac{\mathrm{L}}{\mathrm{f}_{0}}\)(1 + \(\frac{D}{f_{e}}\))

→ Magnifying power of astronomical telescope for
1. nor mal adjustment is:
M = – \(\frac{\mathrm{f}_{0}}{\mathrm{f}_{\mathrm{e}}}\)

2. When final image is formed at least distance of distinct vision:
M = – \(\frac{\mathrm{f}_{0}}{\mathrm{f}_{\mathrm{e}}}\)(1 + \(\frac{\mathrm{f}_{\mathrm{e}}}{\mathrm{D}}\))
where f₀, f_e are the focal lengths of objective and eye piece respectively.
D = least distance of distinct vision.

→ Length of: (a) astronomical telescope tube for normal adjustment is given by
L = f₀ + f_e

(b) Terrestrial telescope is
L = f_o + 4f + f_ee
where f is the focal length of the erecting lens.

→ For a mirror, f = \(\frac{\mathrm{R}}{2}\) , where f, R are the focal length and radius of
curvature of the spherical mirror.

→ Mirror formula is \(\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\)

→ Linear magnification produced by a mirror is
m = \(\frac{\mathrm{I}}{\mathrm{O}}=-\frac{\mathrm{v}}{\mathrm{u}}=\frac{\mathrm{f}}{\mathrm{f}-\mathrm{u}}=\frac{\mathrm{f}-\mathrm{v}}{\mathrm{f}}\)

→ Resolving power of telescope is given by
R.P = \(\frac{\mathrm{d}}{1.22 \lambda}\)

→ Angular limit of resolution of a telescope is
dθ = \(\frac{1}{\text { R.P. }}=\frac{1.22 \lambda}{d}\)

→ Brightness of telescope ∝ πr² ∝ \(\frac{\pi \mathrm{d}^{2}}{4}\)
where d = diameter of the objective lens.

→ Areal magnification = \(\frac{\text { Area of image }}{\text { Area of object }}=\frac{\mathrm{I}^{2}}{\mathrm{O}^{2}}\) = m²

By going through these CBSE Class 12 Hindi Notes Chapter 2 पतंग Summary, Notes, students can recall all the concepts quickly.

पतंग Summary Notes Class 12 Hindi Aroh Chapter 2

पतंग कविता का सारांश

श्री आलोक धन्वा दवारा रचित ‘पतंग’ कविता उनके काव्य-संग्रह ‘दुनिया रोज बनती है’ में संकलित है। इस कविता में कवि ने बाल-सुलभ इच्छाओं एवं उमंगों का सुंदर एवं मनोहारी चित्रण किया है। कवि ने बाल क्रियाकलापों तथा प्रकृति में आए परिवर्तन को अभिव्यक्त करने के लिए अनेक सुंदर बिंबों का समायोजन किया है। पतंग बच्चों की उमंगों का रंग-बिरंगा सपना है, जिसमें वे खो जाना चाहते हैं। आकाश में उड़ती हुई पतंग ऊँचाइयों की वे हदें हैं, जिन्हें बाल-मन छूना चाहता है और उसके पार जाना चाहता है।

कविता एक ऐसी नई दुनिया की सैर कराती है, जहाँ शरद ऋतु का चमकीला सौंदर्य है; तितलियों की रंगीन दुनिया है; दिशाओं के नगाड़े – बजते हैं, छत्तों के खतरनाक कोने से गिरने का भय है तो दूसरी ओर इसी भय पर विजय का ध्वज लहराते बच्चे हैं। ये बच्चे गिर-गिरकर

संभलते हैं तथा पृथ्वी का हर कोना इनके पास आ जाता है। वे हर बार नई पतंग को सबसे ऊँचा उड़ाने का हौसला लिए भादो के बाद शरद की प्रतीक्षा कर रहे हैं। कवि के अनुसार सबसे तेज़ बौछारों के समय का अंधेरा व्यतीत हो गया है और खरगोश की आँख के समान लालिमा – से युक्त सौंदर्यमयी प्रकाशयुक्त सवेरा हो गया है। शरद अनेक झड़ियों को पार करते हुए तथा नई चमकदार साइकिल तेज गति से चलाते हुए जोरों से घंटी बजाते आ गया है। वह अपने सौंदर्य से युक्त चमकीले इशारों से पतंग उड़ाने वाले बच्चों के समूह को बुलाता है।

वह आकाश को इतना सुंदर तथा मुलायम बना देता है कि पतंग ऊपर उठ सके। पतंग जिसे दुनिया की सबसे हल्की और रंगीन वस्तु माना जाता है, वह इस असीम आकाश में उड़ सके। इस हसीन दुनिया का सबसे पहला कागज़ और बाँस की पतली कमानी आकाश में उड़ सके और इनके उड़ने : के साथ ही चारों ओर का वातावरण बच्चों की सीटियों, किलकारियों और तितलियों की मधुर ध्वनि से गूंज उठे।

कोमल बच्चे अपने जन्म से ही कपास के समान कोमलता लेकर आते हैं। ये पृथ्वी भी उनके बेचैन पाँवों के साथ घूमने लगती है। जब । ये बच्चे मकानों की छतों पर बेसुध होकर दौड़ते हैं तो छतों को नरम बना देते हैं। जब ये बच्चे झूला-झूलते हुए आते हैं तो दिशाओं के । नगाड़े बजने लगते हैं। प्राय: बच्चे छतों पर तेज गति से बेसुध होकर दौड़ते हैं तो उस समय उनके रोमांचित शरीर का संगीत ही उन्हें गिरने से बचाता है। उस समय मात्र धागे के सहारे उडते पतंगों की ऊँचाइयाँ उन्हें सहारा देकर थाम लेती हैं।

असीम आकाश में पतंगों की ऊँचाइयों के साथ-साथ ये कोमल बच्चे भी अपने रंध्रों के सहारे उड़ रहे हैं। कवि का मानना है कि अगर बच्चे छतों के खतरनाक किनारों से गिरकर बच जाते हैं तो उसके बाद वे पहले से ज्यादा निडर होकर स्वर्णिम सूर्य के सामने आते हैं। तब उनके इस साहस, धैर्य | और निडरता को देखकर यह पृथ्वी भी उनके पैरों के पास अधिक तेजी से घूमती है।

पतंग कवि परिचय

जीवन-परिचय-श्री आलोक धन्वा समकालीन हिंदी साहित्य के प्रमुख कवि माने जाते हैं। ये सामाजिक ० चेतना से ओत-प्रोत कवि हैं। इनका जन्म सन् 1948 ई० में बिहार राज्य के मुंगेर जिले में हुआ था। इनकी साहित्य-सेवा के कारण इन्हें राहुल सम्मान से अलंकृत किया गया। इन्हें बिहार राष्ट्रभाषा परिषद 10 का साहित्य सम्मान और बनारसी प्रसाद भोजपुरी सम्मान से भी सम्मानित किया गया है।

रचनाएँ-आलोक धन्वा एक कवि के रूप में उन्हें विशेष ख्याति प्राप्त हैं। उनकी लेखनी अबाध गति से साहित्य-सृजन हेतु चल रही है। उनकी प्रमुख रचनाएँ निम्नलिखित हैं

(i) काव्य-जनता का आदमी (उनकी पहली कविता है, जो सन् 1972 में प्रकाशित हुई) भागी हुई लड़कियाँ, ब्रूनों की बेटियाँ, गोली दागो पोस्टर आदि। ब्रूनों की बेटियाँ से कवि को बहुत 10 प्रसिद्धि प्राप्त हुई है।

(ii) काव्य-संग्रह-दुनिया रोज बनती है (एकमात्र संग्रह)। साहित्यिक विशेषताएँ–आलोक धन्वा समकालीन काव्य-जगत के विशेष हस्ताक्षर हैं। ये एक संवेदनशील व्यक्ति हैं। इनका साहित्य समकालीन समाज की संवेदना से ओत-प्रोत है। ये सातवें-आठवें दशक के जन-आंदोलनों से अत्यंत प्रभावित हुए, इसलिए इनके काव्य में समाज का यथार्थ चित्रण मिलता है। इनके साहित्य में राष्ट्रीय चेतना का भाव प्रमुखता से झलकता है।

इन्होंने अपने साहित्य में भारतीय संस्कृति एवं समाज का अनूठा चित्रांकन प्रस्तुत किया है। इनके मन में अपने देश के प्रति गौरव की भावना है। यही गौरवपूर्ण भावना इनके साहित्य में झंकृत होती है। आलोक धन्वा बाल मनोविज्ञान के कवि हैं। इन्होंने भाग-दौड़ की जिंदगी में उपेक्षित बाल-मन को जाँच-परखकर उसका अनूठा चित्रण किया है। ‘दुनिया रोज बनती है’ काव्य-संग्रह की ‘पतंग’ कविता में बाल-सुलभ चेष्टाओं एवं क्रियाकलापों का सजीव एवं मनोहारी अंकन हुआ है।  इन्होंने अपने साहित्य में शुद्ध साहित्यिक खड़ी बोली भाषा का प्रयोग किया है।

इसके साथ-साथ इसमें संस्कृत के तत्सम, तद्भव, साधारण बोलचाल और विदेशी भाषाओं के शब्दों का भी प्रयोग हुआ है। इनके काव्य में कोमलकांत पदावली का भी सजीव चित्रण हुआ है। इनकी अभिधात्मक शैली भावपूर्ण है। प्रसाद गुण के साथ-साथ माधुर्य गुण का भी समायोजन हुआ है। इनकी भाषा-शैली में अनुप्रास, स्वभावोक्ति, पदमैत्री, स्वरमैत्री, यमक, उपमा, रूपक, मानवीकरण आदि अलंकारों का प्रयोग मिलता है। आलोक धन्वा समकालीन काव्यधारा के प्रमुख कवि हैं। इनका समकालीन हिंदी कविता में प्रमुख स्थान है।

By going through these CBSE Class 12 Physics Notes Chapter 8 Electromagnetic Waves, students can recall all the concepts quickly.

Electromagnetic Waves Notes Class 12 Physics Chapter 8

→ Displacement current is a 1 ways equal to charging (for discharging) current and lasts so long as the capacitor (producing varying electric field) is charged or discharged.

→ An accelerated charged particle emits e.m. waves.

→ \(\overrightarrow{\mathrm{S}}\) = \(\overrightarrow{\mathrm{E}}\) × \(\overrightarrow{\mathrm{B}}\) is called Poynting vector acts in a direction perpendicular to the plane of \(\overrightarrow{\mathrm{E}}\) and \(\overrightarrow{\mathrm{B}}\) .

→ The displacement current is named so because it is produced by the displacement of electrons caused by changing electric fields.

→ X-rays have the shortest wavelength (≈ 1 Å).

→ The charging or discharging current is called conduction current.

→ The amplitude of electric and magnetic fields in free space in e.m. waves are related as E = CB

→ Electric vector is called light vector as it is responsible for the optical effect of e.m. wave.

→ The energy of the e.m. wave is shared equally between the electric field vector and the magnetic field vector.

→ Microwaves are very commonly used in radar to locate flying objects like airplanes, jet planes, etc.

→ Tire earth’s atmosphere produces Green House effect. In the absence of the earth’s atmosphere, the temperature on earth during the day will increase and during the night it would decrease.

→ The ozone layer which is present in the stratosphere protects the earth from high-energy radiations coming from outer space.

→ The velocity of em. waves in a medium is given by
v = \(\frac{1}{\sqrt{\mu_{0} \varepsilon_{0} \mu_{\mathrm{r}} \varepsilon_{\mathrm{r}}}}=\frac{C}{\sqrt{\mu_{\mathrm{r}} \varepsilon_{\mathrm{r}}}}\)

→ There is no conduction current in a traveling e.m. wave.

→ Earth’s atmosphere is transparent to visible light and most of the infrared rays are absorbed by the atmosphere.

→ Radio waves were discovered by Hertz and are used in communication.

→ e.m. waves are transverse in nature.

→ e.m. waves exert pressure on the objects on which they fall as they carry energy and momentum.

→ The wavelength range of em. waves are from 10^-15 m to 10⁹ m and the frequency range is 10²⁴ Hz to 1 Hz.

→ Green House Effect takes place due to the heating of the earth’s atmosphere due to the trapping of infrared rays by the CO₂ layer in the atmosphere.

→ Modified Ampere Circuital law: It states that the line integral of the magnetic field around a closed path is always equal to μ0 times the sum of the conduction dnd displacement currents i.e.,

→ Displacement Current: It is defined as the current produced in a region where a change of electric flux takes place due to the change in electric field intensity in that region.

Important Formulae

→ Amper’s circuital law states that
∫ \(\overrightarrow{\mathrm{B}}\).\(\overrightarrow{\mathrm{dl}}\) = μ₀ I_C
where I_C = conduction current Displacement current is given by

→ Displacement current is given by
I_D = ε₀ \(\frac{\mathrm{d} \phi_{\mathrm{E}}}{\mathrm{dt}}\)

→ C = \(\frac{E_{0}}{B_{0}}=\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}\)

→ Energy density of electric field, UE = \(\frac{1}{2}\) ε₀ E²

→ Energy density of electric field, UB = \(\frac{\mathrm{B}^{2}}{2 \mu_{0}^{2}}\)

→ Intensity of e.m. wave is given by
I = average energy density × speed of e.m. wave
= \(\frac{1}{2}\) ε₀E² × C = ρ/4πr²

→ \(\overrightarrow{\mathrm{B}}\) at a point between the plates of the capacitor at a distance r from its axis is given by.
B = \(\frac{\mu_{0} \mathrm{Ir}}{2 \pi \mathrm{R}^{2}}\)
Where R = radius of each circular plate of the capacitor.

→ Velocity of e.m. waves is
C = vλ

→ An electromagnetic wave of frequency v, wavelength λ propagating along the z-axis, we have

→ The speed of light or of electromagnetic waves in a material medium is given by
υ = \(\frac{1}{\sqrt{\mu \varepsilon}}\)
where μ is the permeability of the medium and ε is its permittivity.

→ Bmax = \(\frac{\mu_{0} I_{D}}{2 \pi R}\)

By going through these CBSE Class 12 Physics Notes Chapter 7 Alternating Current, students can recall all the concepts quickly.

Alternating Current Notes Class 12 Physics Chapter 7

→ In a pure ohmic resistance both alternating current and e.m.f. are in the same phase.

→ Alternating e.m.f. leads the alternating current by \(\frac{π}{2}\) in a pure inductance.

→ In a pure capacitor circuit, the alternating e.m.f. lags behind the alternating current by \(\frac{π}{2}\).

→ x_L = ωL is called inductive reactance.

→ x_C = \(\frac{1}{\omega C}\) is called capacitance reactance.

→ Resistance, reactance, and impedance all are measured in ohm.

→ The graph between x_L and ω is a straight line.

→ The applied voltage is equal to the potential drop across the resistance R at the resonant frequency in the LCR circuit.

→ Power is dissipated only due to the ohmic resistance in an a.c. circuit.

→ Thus in an RC or RL a.c. the circuit power is dissipated only due to R and not due to its inductance or capacitance.

→ Resonant angular frequency is the same both for the series and parallel resonant circuit.

→ The graph between xC and w is a hyperbola.

→ The maximum value of current is I = \(\frac{E_{\mathrm{rms}}}{\mathrm{R}}\)at the resonant angular frequency W = W₀.

→ As ω to increases, Z of parallel LCR resonant circuit first increases becomes maximum and then decreases.

→ For series LCR resonant circuit, Z first decreases become minimum and then increases.

→ The power rating of an element used in a.c. circuit refers to its average power rating.

→ The power consumed in an a.c. the circuit is never negative.

→ For very high frequency of a.c., the inductor behaves as an open circuit and the capacitor behaves as a conductor.

→ The impedance of the LR circuit depends upon the frequency of a.c. The phase angle between E and I in an LR circuit also depends upon the frequency.

→ As the frequency of a.e. increases, the impedance of the CR circuit decreases.

→ Electrical resonance takes place when the amplitude of the current in the circuit is maximum and impedance is minimum and the LCR circuit is a purely resistive circuit.

→ For purely resistive circuit, power factor = 1.

→ For purely inductive and capacitive circuits, the power factor is zero. Choke coil is used to control a.c. without much loss of electric power.

→ K > 1 for step-up transformer and K < 1 for step down transformer. Transformer works on the principle of mutual inductance. q = 100% and E_pl_p = E_sI_s for an ideal transformer.

→ The power consumed in a circuit is never negative.

→ A.C.: It is defined as the? electric current magnitude of which changes with time and reverses its direction periodically.

→ Average or Mean Value of A.C.: It is defined as that steady current which when passed through a circuit for a half time period of A.C. produces the same amount of charge as is being produced by A.C. in the same time and in the same circuit.

→ R.M.S. value or effective value of A.C.: It is defined as that steady current that produces the same amount of heat in resistance in a given time as is being done by a.c. passed through the same circuit for the same time.

→ Inductive reactance: It is the effective opposition offered by the inductor to the flow of a.c. in the circuit.

→ Capacitive reactance: -It is the effective opposition offered by the capacitor to the flow of a.c. in the circuit.

→ Q-factor of series LCR circuit: It is defined as the ratio of the voltage drop across inductor (or capacitor) to the applied voltage.

→ Power of an a.c. circuit: It is the product of instantaneous e.m.f. and instantaneous current in the circuit.

→ Power factor: It is defined as the ratio of average power to the apparent power.

→ Idle or wattless current: It is the current due to the flow of which no power is consumed in an a.c. circuit.

→ Transformer’s a device used to convert low alternating voltage at high current into a high voltage at low current or vice-versa.

Important Formulae

→ E_rms = \(\frac{1}{\sqrt{2}}\) E₀ = E _virtual = E_eff

→ Irms = \(\frac{1}{\sqrt{2}}\) I₀

→ Instantaneous e.m.f. is given by E = E₀ sin ωt

→ In a purely inductive circuit, current lags behind E by \(\frac{π}{2}\)
I = I₀ sin (ωt – \(\frac{π}{2}\))

→ In a purely capacitive circuit
I = I₀ sin (ωt + \(\frac{π}{2}\))

→ X_L = ωL = 2πvL = \(\frac{\mathrm{E}_{0}}{\mathrm{I}_{0}}=\frac{\mathrm{E}_{\mathrm{v}}}{\mathrm{F}_{v}}\)

→ X_L = \(\frac{1}{\omega C}=\frac{1}{2 \pi v C}=\frac{E_{0}}{I_{0}}=\frac{E_{v}}{I_{v}}\)

→ Average value of induced a.c. over a complete cycle is:

→ Average power = apparent power × power factor
or
P_av = E_v I_v cos Φ.

→ cos Φ = \(\frac{\mathrm{R}}{\mathrm{Z}}\)

→ Resonant angular frequency of LCR series circuit is given by
ω₀ = \(\frac{1}{\sqrt{\mathrm{LC}}}\)
or
v₀ = \(\frac{1}{2 \pi \sqrt{L C}}\)

→ Impedence of LCR series circuit is given by
Z = \(\sqrt{R^{2}+\left(X_{L}-X_{C}\right)^{2}}\)
= \(\sqrt{R^{2}+\left(\omega L-\frac{1}{\omega C}\right)^{2}}\)

→ Tangent of the phase angle is given by .
tan Φ = \(\frac{X_{L}-X_{C}}{R}\)

→ Power factor of LR circuit is given by
cos Φ = \(\frac{R}{Z}=\frac{R}{\sqrt{R^{2}+X_{L}^{2}}}\)
tan Φ = \(\frac{\mathrm{x}_{\mathrm{L}}}{\mathrm{R}}=\frac{\omega \mathrm{L}}{\mathrm{R}}\)

→ For CR. circuit,
tan Φ = \(\frac{X_{C}}{R}=\frac{1}{R \omega C}\)
Z = \(\sqrt{R^{2}+X_{c}^{2}}=\sqrt{R^{2}+\left(\frac{1}{\omega C}\right)^{2}}\)

→ For a transformer,
K = \(\frac{\mathrm{N}_{\mathrm{s}}}{\mathrm{N}_{\mathrm{p}}}=\frac{\phi_{\mathrm{s}}}{\dot{\phi}_{\mathrm{p}}}=\frac{\mathrm{E}_{\mathrm{s}}}{\mathrm{E}_{\mathrm{p}}}=\frac{\mathrm{I}_{\mathrm{p}}}{\mathrm{I}_{\mathrm{s}}}\)

→ For an ideal transformer,

When Z_p and Z_s are called impedance of primary and secondary coil of the transformer.

→ Efficiency of a transformer is given by,
η = \(\frac{\text { output power }}{\text { input power }}\)
= \(\frac{\mathrm{E}_{\mathrm{s}} \mathrm{I}_{\mathrm{s}}}{\mathrm{E}_{\mathrm{p}} \mathrm{I}_{\mathrm{p}}}\).

→ Maximum e.m.f. induced in a coil is given by e₀ = NBAω.
where N = No. of turns of the coil.
A = Area of the coil.
ω = angular frequency of rotation of the coil.
B = magnetic field.

→ Q.factor = \(\frac{\mathrm{X}_{\mathrm{L}} \mathrm{I}}{\mathrm{RI}}=\frac{\omega_{0} \mathrm{~L}}{\mathrm{R}}=\frac{1}{\omega_{0} \mathrm{CR}}=\frac{1}{\mathrm{R}} \sqrt{\frac{\mathrm{L}}{\mathrm{C}}}\)

By going through these CBSE Class 12 Physics Notes Chapter 6 Electromagnetic Induction, students can recall all the concepts quickly.

Electromagnetic Induction Notes Class 12 Physics Chapter 6

→ An induced e.m.f. is produced in a conductor when it moves through a magnetic field.

→ The induced e.m.f. may also be produced when a stationary conductor is placed in a changing magnetic field.

→ Lenz’s law explains the cause of induced e.m.f.

→ Electromagnetic induction (E.M.L) converts mechanical energy into electrical energy.

→ inductance in the electrical circuit is equivalent to the inertia or mass in mechanics.

→ The dimensional formula of inductance is [ML² T^-2 A^-2].

→ The magnetic flux is a scalar quantity and has the dimensions of [ML² T^-2 A^-1].

→ The inductance of a coil depends on the

1. across of cross-section of the coil.
2. no. of turns in the coil.
3. permeability of the core of the coil.

→ The direction of induced current can be obtained by Fleming’s right rule.

→ When the magnetic flux through a circuit changes, an induced e.m.f. is produced in it and it lasts so long as the change in the magnetic flux takes place.

→ Eddy currents are set up in any conducting material placed in a varying magnetic field.

→ Eddy currents produce heat at the cost of electrical power and thus reduce power efficiency.

→ Eddy currents can be minimized by using eddy currents.

→ S.I. unit of Φ is weber (Wb).
I Wb = Tm² = 1 Tesla × 1 m².

→ S.L. unit of L and M is henry (H).

→ 1 H = 1 VA^-1 s.

→ The mutual inductance of two coils depends upon the shape, size, or geometry of two coils and the no. of turns in the two coils.

→ The area of cross-section and length of two coils affect the ‘M’ between two coils.

→ No current flows in a rectangular closed loop moving horizontally in a uniform magnetic field as long as the loop is completely in the magnetic field.

→ Eddy currents don’t cause sparks.

→ Faraday’s flux rule: It states that the induced e.m.f. produced in a closed circuit is directly proportional to the rate of change of the magnetic flux linked with it.
i.e., e ∝ \(\frac{\mathrm{d} \phi}{\mathrm{d} \mathrm{t}}\)
or
e = – \(\frac{\mathrm{d} \phi}{\mathrm{d} \mathrm{t}}\)
when – ve sign shows that ‘e’ acts in a direction opposite to the direction of change in magnetic flux.

→ Lenz’s law: It states that the induced e.m.f. always acts in such a direction so as to opposite the very cause producing it.

→ Self-induction: It is defined as the property of an electrical circuit due to which it opposes the change in the current in the circuit.

→ Self-inductance of a coil: 11 is defined as the magnetic flux linked with a coil when unit current flows through it. It is also equal to the induced e.m.f. produced in the coil when the rate of change of current is unity through it.

→ Mutual inductance of two coils: It is the property of producing induced e.m.f. in a coil by changing the current or magnetic flux linked with the neighboring coil.

→ Coefficient of Mutual induction: It is equal to induced e.m.f. of one coil when the rate of change of current is unity in the neighboring coil.

Important Formulae

→ Φ = \(\overrightarrow{\mathrm{B}}\) . \(\overrightarrow{\mathrm{A}}\) = BA cos θ
where Φ = magnetic flux,
\(\overrightarrow{\mathrm{A}}\) = surface area,
\(\overrightarrow{\mathrm{B}}\) = magnetic field.

→ E or e = – \(\frac{\mathrm{d} \phi}{\mathrm{dt}}\) for one turn and e – \(\frac{\mathrm{Nd} \phi}{\mathrm{dt}}\) for N. turn of a coil.

→ Induced current is given by
I = \(\frac{\mathrm{e}}{\mathrm{R}}=-\frac{\mathrm{N}}{\mathrm{R}} \cdot \frac{\mathrm{d} \phi}{\mathrm{dt}}\)

→ When the magnetic field is parallel to the outward normal to the surface of the coil, then the change in the magnetic flux due to change in field is:
dΦ = Φ₂ – Φ₁ = B₂A – B₁A = (B₂ – B₁)A

→ Charge induced in a circuit is
q = \(\frac{\mathrm{d} \phi}{\mathrm{R}}=\frac{\text { Change in magnetic flux }}{\text { Resistance of circuit }}\)

→ Motional e.m.f. is: e = Blυ.

→ Induced current produced = Blυ/R

→ ε = – L \(\frac{\mathrm{dI}}{\mathrm{dt}}\); L = Self-inductance

→ Force required to pull a rod out of magnetic field is
F = \(\frac{B^{2} l^{2} v}{R}\)

→ e = – M\(\frac{\mathrm{dI}}{\mathrm{dt}}\), M = Mutual inductance.

→ Induced e.m.f. in a coil rotating with angular speed ω in a magnetic field B is e = NBA ω sin ωt. .
e₀ = NBAω = max. e.m.f. induced.

→ Self inductance of a long solenoid is given by
L = μ₀ n² Al = \(\frac{\mu_{0} \mathrm{~N}^{2} \mathrm{~A}}{l}\)

→ Mutual inductance of two coils is given by
M = μ₀ n₁ n₂ Al
= \(\frac{\mu_{0} \mathrm{~N}_{1} \mathrm{~N}_{2} \mathrm{~A}}{l}\)
where l = length of primary coil.
A = Area of a cross-section of each coil.

→ The inductance of coils in series is given by
L = L₁ + L₂ + L₃ + …………

→ The inductance of coils in parallel is given by
\(\frac{1}{L_{P}}=\frac{1}{L_{1}}+\frac{1}{L_{2}}+\frac{1}{L_{3}}+\ldots\)

→ Induced charge in terms of B is given by:
q = \(\frac{\mathrm{NBA}}{\mathrm{R}}\)

→ Induced current is given by
I = \(\frac{\mathrm{NA}}{\mathrm{R}}\)(B₁ – B₂)

→ Also induced charge is given by
q = It = \(=\frac{\mathrm{e}}{\mathrm{R}}\) t

→ If two coils of inductances L1 and L2 are coupled together, then
M = k \(\sqrt{\mathrm{L}_{1} \mathrm{~L}_{2}}\)
where k is called coupling constant,

→ k = 1 for perfectly coupled coils.

→ Two coils are said to be perfectly coupled when the magnetic flux of one coil is completely linked with the second coil.

→ Magnetic energy stored in a coil of inductance L is given by
U = \(\frac{1}{2}\) LI².

→ ‘e’ produced between the ends of a rod rotating about an end perpendicular to the magnetic field is given by
e= \(\frac{1}{2}\) BWl² = BA.f, f=frequency.

By going through these CBSE Class 12 Physics Notes Chapter 5 Magnetism and Matter, students can recall all the concepts quickly.

Magnetism and Matter Notes Class 12 Physics Chapter 5

→ Magnetic induction (B) and magnetic intensity (H) are related as B = μH.

→ B is expressed in testa (T) and gauss (G) in S.I. and C.G.S. systems respectively.

→ H in a vacuum is expressed in overstated (C.G.S. system) and Am^-1 in S.I. system.

→ The angle of dip at poles is 90° and at the equator, it is zero.

→ S.I. unit of pole strength (m) is NT^-1 or Am.

→ The value of angle of dip and declination not only charges from place to place but also at the same place, they change from time to time.

→ Diamagnetism originates from the magnetic moment associated with the orbital motion of electrons.

→ Paramagnetism and Ferromagnetism are associated with the magnetic moment of the spinning electrons.

→ Ferromagnetism depends on temperature. It decreases with an increase in temperature. At a certain temperature called the curie point, the ferromagnetic substance is converted into a paramagnetic substance.

→ The magnetic lines of force always form closed and continuous loops both inside and outside the bar magnet.

→ The magnetic susceptibility of a diamagnetic substance is independent of temperature.

→ The hysteresis cycle for the core of a transformer should be narrow and large in height.

→ The end of the freely suspended magnet pointing towards the north of the earth is called the north pole of the magnet and the end pointing towards the south pole is called the south pole of the magnet.

→ The north and south pole of a magnet is always of equal strength.

→ Monopole never exists.

→ For all purposes, we can consider the magnetic field of a bar magnet and a straight solenoid to be identical.

→ The field inside the solenoid is stronger than the field inside a bar magnet.

→ The earth’s magnetic field at any place is a vector quantity and it requires three parameters to describe it. These are called magnetic elements of the earth.

→ 1 G = 10^-4 T.

→ 10 posted = 80 Am^-1.

→ The geometric length of a magnet is always more than the magnetic length.

→ A magnetic dipole is the simplest magnetic structure that is known to exist in nature.

→ The strength of the magnetic field of a solenoid can be increased or decreased by adjusting the current and the direction of the magnetic field can be changed by changing the direction of the current.

→ S I. unit of magnetic dipole moment is Joule/tesla (JT^-1) or Weber- meter (Wb-m) or Ampere metre² (Am²).

→ S.I. unit of magnetic flux is weber (Wb).

→ S.I. unit of magnetic permeability (p) is Tm^-1 A.

→ X_m has no units.

→ Another S.I. unit of magnetic intensity (H) is N Wb^-1.

→ S.I. unit of Intensity of magnetization (I) is Am^-1.

→ S.I. unit of Torque and P.E. is Joule (J).

→ S.I. unit of energy dissipated in hysteresis loop is J m^-3 cycle^-1.

→ B is also called magnetic flux density and has an S.I. unit in Tesla (T).

→ The unit pole is defined as one which when placed in vacuum at a distance of 1 m from an equal and similar pole exerts a force of \(\frac{\mu_{0}}{4 \pi}\) or 10^-7 N on it.

→ Magnetic elements: They are the physical quantities that are required to completely specify the earth’s magnetic field at a point, e.g., dip, declination, and B_H.

→ Declination at a place: It is defined as the angle between geographical and magnetic meridian at that place.

→ Dip at a place: It is defined as the angle made by the resultant earth’s magnetic field with the horizontal direction.

→ The intensity of induced magnetization: It is defined as the magnetic moment developed per unit volume of the magnetic material. Its value depends on the media in which it is magnetized.

→ Magnetic susceptibility of a given material. It is defined as the ratio of the intensity of magnetization and magnetizing field.
i.e., χ_m = \(\frac{I}{H}\)

→ The intensity of magnetization (I): It is defined as the magnetic moment developed per unit volume when a magnetic substance is subjected to the magnetizing field.
i.e., I = \(\frac{\mathrm{M}}{\mathrm{V}}=\frac{\mathrm{m} \cdot 2 l}{\mathrm{a} \cdot \mathrm{zl}}=\frac{\mathrm{m}}{\mathrm{a}}\)

→ I is also defined as the pole strength developed per unit area of cross-section of the specimen.

→ Magnetic Induction (B): It is defined as the total no. of magnetic lines of induction (magnetic field lines inside the material) crossing per unit area normally through the magnetic substance.

→ Magnetic permeability (μ): It is the ratio of magnetic induction to the magnetic intensity,
i.e., μ = \(\frac{B}{H}\)

→ Curie’s law: States that the magnetic susceptibility of a paramagnetic material is inversely proportional to its absolute temperature.

→ Curie point: It is defined as the temperature at which a ferromagnetic substance starts behaving as a paramagnetic substance. It is also called Curie temperature.

→ Hysteresis: It is the lag of intensity of magnetization behind the magnetizing field during the magnetization and demagnetization of the ferromagnetic substance.

→ Coercivity and retentivity are also associated with the hysteresis loop.

→ Coulomb’s law of magnetic force: It states that
F ∝ \(\frac{m_{1} m_{2}}{r^{2}}\)
or
F = \(\frac{\mu_{0}}{4 \pi} \cdot \frac{m_{1} m_{2}}{r^{2}}\)

Important Formulae

→ Torque experienced by a magnet or a magnetic dipole in a uniform magnetic field is
τ = | \(\overrightarrow{\mathrm{M}}\) × \(\overrightarrow{\mathrm{B}}\) | = MB sin θ

→ M = magnetic moment, B = magnetic field, θ = angle between \(\overrightarrow{\mathrm{M}}\) and \(\overrightarrow{\mathrm{B}}\).

→ Magnetic dipole moment due to current loop is:
M = nIA
where n = no. of turns in it, I = current, A = area of loop.

→ Work done in rotating a magnet placed in a magnetic field from θ₁ to θ₂ is
W = MB (cos θ₁ – cos θ₂)

→ Gauss’s law of magnetism states that
∮_s \(\overrightarrow{\mathrm{B}}\). \(\overrightarrow{\mathrm{dS}}\) = 0

→ Magnetic field due to a magnetic diple at a point on its axis at a distance r from its centre is :
B = \(\frac{\mu_{0}}{4 \pi} \cdot \frac{2 \mathrm{M}}{\mathrm{r}^{3}}\)

→ On equitorial line
B = \(\frac{\mu_{0}}{4 \pi} \cdot \frac{\mathrm{M}}{\mathrm{r}^{3}}\)

→ If the magnet is not short, then
B = \(\frac{\mu_{0}}{4 \pi} \cdot \frac{2 \mathrm{Mr}}{\left(\mathrm{r}^{2}-l^{2}\right)}\) on axial line

→ B equitorial = \(\frac{\mu_{0}}{4 \pi} \cdot \frac{\mathrm{M}}{\left(\mathrm{r}^{2}+l^{2}\right)^{3 / 2}}\)

→ Time period of an oscillating magnet along earth’s magnetic field is given by –
T = 2π \(\sqrt{\frac{I}{M B_{H}}}\)
when I=M.I.of magnet = m \(\left(\frac{l^{2}+b^{2}}{12}\right)\)

→ Magnetic induction is given by
B = μ₀ (H + I)

→ B in vacuum is given by
B = μ₀H

→ μ = \(\frac{B}{H}\)

→ χ_m = \(\frac{I}{H}\)

→ μ = (1 + χ_m)
or
μ = μ₀(1 + χ_m)

→ I = C\(\frac{H}{T}\)

→ μ_r = \(\frac{\mu}{\mu_{0}}\)

→ B_H = B cos δ

→ B_v = B sin δ

→ tan δ = \(\frac{\mathrm{B}_{\mathrm{v}}}{\mathrm{B}_{\mathrm{H}}}\)
where B_H and B_V are the horizontal and vertical components of earth’s total magnetic field at a point.
δ = angle of dip at that place

→ B = \(\sqrt{B_{H}^{2}+B_{V}^{2}}\)

→ B_H = B magnet at the neutral point.

→ Magnetic field due to a straight current carrying cable at a point at a distance r from it is given by:
B = \(\frac{\mu_{0}}{4 \pi} \cdot \frac{2 I}{r}\)

→ \(\frac{\mathrm{M}_{2}}{\mathrm{M}_{1}}=\frac{\mathrm{T}_{l}^{2}-\mathrm{T}_{1}^{2}}{\left(\mathrm{~T}_{2}^{2}+\mathrm{T}_{1}^{2}\right)}\)
where M₁ and M₂ are magnetic moments of two magnetic field in the vibration magnetometor stirrup with unlike poles in the same direction having time period of T combination T₂
T₁ = Time period of the combination of two magnetic having like poles in the same direction.

→ tangent law is
B = B_H tan θ
where B and B_H are the two mutually perpendicular magnetic fields.
θ = angle made by the magnet with B_H.

→ I = k tan θ for tangent galvanometer where K = \(\frac{\mathrm{B}_{\mathrm{H}}}{\mathrm{a}}=\frac{2 \mathrm{rB}_{\mathrm{H}}}{\mu_{0} \mathrm{~N}}\) is the reduction factor.

→ Magnetic field at a point due to a Rowland ring is given by
B = μ₀ μ_r n I
where n = no. of turns per unit length.
I = current in the ring.

By going through these CBSE Class 12 Physics Notes Chapter 4 Moving Charges and Magnetism, students can recall all the concepts quickly.

Moving Charges and Magnetism Notes Class 12 Physics Chapter 4

→ An electric charge at rest produces an electric field around it while a moving charge produces both electric and magnetic fields.

→ A magnet at rest produces a magnetic field around it.

→ An oscillating, as well as an accelerated charge, produces e.m. waves.

→ No poles are produced in a coil carrying current but such a coil shows N and S polarities.

→ 1T = 10⁴ G = 1 Wb m^-2 = 10⁴ maxwell cm^-2.

→ A current-carrying conductor has a magnetic field and not an electric field around it.

→ Work done in moving a unit pole around a long conductor is
W = μ₀ I

→ The torque acting on the loop is independent of its shape but depends on the area of the loop.

→ Path of a charged particle in a magnetic field ( \(\overrightarrow{\mathrm{B}}\) ) is a straight line when it moves parallel or anti-parallel to \(\overrightarrow{\mathrm{B}}\) and is a circle when moves perpendicular to \(\overrightarrow{\mathrm{B}}\)

→ Two parallel conductors with currents in the same direction attract each other which is a magnetic interaction and if the current flows in them in opposite direction, then they repel each other.

→ Magnetic force is always normal to the field.

→ Magnetic force is not a central force.

→ A long straight current-carrying cylinder for an external point behaves like a straight current-carrying wire.

→ If the battery is connected to two points A and B of a conducting ring, the magnetic field at the center due to the current in the ring is zero.

→ A long coil of wire is called a solenoid. Its magnetic field is similar to that of the magnet.

→ The electric field is conservative in nature and ∮ \(\overrightarrow{\mathrm{E}}\).\(\overrightarrow{\mathrm{dl}}\)= 0 but the magnetic field is not conservative as ∮ \(\overrightarrow{\mathrm{B}}\). \(\overrightarrow{\mathrm{dl}}\) = μ₀ I.

→ The total force on a planar current loop in a magnetic field is always zero.

→ The radius of a charged particle moving in a magnetic field is directly proportional to its momentum.

→ Speed or K.E. of the particle always remains constant in \(\overrightarrow{\mathrm{B}}\) as \(\overrightarrow{\mathrm{F}_{\mathrm{m}}}\) is perpendicular to \(\overrightarrow{\mathrm{B}}\) .

→ The nature of a circular path followed by a charged particle moving in a given magnetic field depends upon the following:

1. Direction of \(\overrightarrow{\mathrm{B}}\),
2. The direction of motion of the charged particle,
3. Nature of charge.

→ For a positively charged particle moving towards RHS in a downward \(\overrightarrow{\mathrm{B}}\), the circular path is anticlockwise and for a negatively charged particle, it is clockwise.

→ The \(\overrightarrow{\mathrm{B}}\) is uniform (except near the ends) for a sufficiently long solenoid and is independent of its length and area of cross-section.

→ Cyclotron cannot be used to accelerate electrons.

→ A galvanometer is a low resistance instrument.

→ It can be converted into an ammeter by connecting a small resistance parallel to it.

→ Ammeter is always connected in series in the circuit.

→ A galvanometer is converted into a voltmeter by connecting a high resistance in series. The voltmeter is always connected in parallel to the circuit.

→ Two parallel streams of protons with protons moving in the same direction repel each other. There is an electric as well as magnetic interaction. The electric interaction gives repulsive force while the magnetic interaction gives an attractive force. As F_e > F_m, so there is a net repulsion between them.

→ When the above raid stream moves in the opposite direction, then they repel each other.

→ F_e and F_m being repulsive, so there is a net repulsive force between them.

→ The minimum potential difference across the terminals of the galvanometer for full-scale deflection is
V_g = I_g G.

→The potential diff. V across the terminals of a combination of R and G is V = I_g (R + G).

→ \(\frac{\mathrm{V}}{\mathrm{V}_{\mathrm{g}}}=\frac{\mathrm{R}-\mathrm{G}}{\mathrm{G}}\) is called voltage multiplying power of series resistance R and denoted as n.
∴ n = \(\frac{V}{V_{g}}=\frac{R+G}{G}\) ⇒ R = G (n – 1).

→ R_v = R + G = nG.

→ Fleming’s left-hand rule helps us to know the direction of the force on a moving charge or on a current-carrying conductor placed in a uniform magnetic field.

→ Current element: It is the product of current and the length of conductor carrying current i.e., current element = I. \(\overrightarrow{\mathrm{l}}\) .It is a vector quantity acting along I.

→ The direction in a magnetic field along which the current-carrying conductor experiences no force is called the direction of the magnetic field.

→ Pitch of the helix (p): It is defined as the distance traveled by the particle along the magnetic field in one revolution i.e., in a time T.
∴ p = υ cos θ × T = υ cos θ. \(\frac{2 \pi m}{B q}=\frac{2 \pi m v \cos \theta}{B q}\)

→ Shunt: It is a small resistance connected in parallel to the galvanometer.

Important Formulae

→ \(\overrightarrow{\mathrm{B}}\) due to a straight current carrying conductor is given by
\(\overrightarrow{\mathrm{B}}\) = \(\frac{\mu_{0} \mathrm{I}}{4 \pi \mathrm{a}}\)(sin Φ₁ + sin Φ₂)

→ For infinitely long conductor,
\(\overrightarrow{\mathrm{B}}\) = \(\frac{\mu_{0}}{4 \pi} \cdot \frac{2 \mathrm{I}}{\mathrm{a}}\)
where a = perpendicular distance of the point from the conductor
I = current in the conductor

→ \(\overrightarrow{\mathrm{B}}\) at a point on the axis of a current carrying loop of n turns at a distance x from its centre is given by
\(\overrightarrow{\mathrm{B}}\) = \(\frac{\mu_{0} \mathrm{nIR}^{2}}{2\left(\mathrm{x}^{2}+\mathrm{R}^{2}\right)^{\frac{3}{2}}}\)
where R = radius of loop

→ \(\overrightarrow{\mathrm{B}}\) at its centre is given by
B = \(\frac{\mu_{0} \mathrm{nIR}^{2}}{2 \mathrm{R}^{3}}=\frac{\mu_{0} \mathrm{nI}}{2 \mathrm{R}}\)

→ Magnetic field inside a solenoid having n tums/length is given by
B = µ₀ nI.

→ \(\overrightarrow{\mathrm{B}}\) at a point near its end is given by
B = \(\frac{1}{2}\) µ₀ nI

→ Maximum energy attained by a particle in a cyclotron is:
Emax = \(\frac{\mathrm{e}^{2} \mathrm{~B}^{2} \mathrm{r}_{\max }^{2}}{2 \mathrm{~m}}\)

→ Potential difference required to accelerate an electron is
V = \(\frac{B^{2} r^{2} e}{2 m}\)

→ Force on a charge moving in \(\overrightarrow{\mathrm{B}}\) is
\(\overrightarrow{\mathrm{F}_{\mathrm{m}}}\) = q(\(\overrightarrow{\mathrm{υ}}\) × \(\overrightarrow{\mathrm{B}}\))
F_max = qυB

→ Force between two moviiig dia rges s
F = \(\frac{\mu_{0}}{4 \pi} \cdot \frac{\mathrm{q}_{1} \mathrm{q}_{2} v_{1} v_{2}}{\mathrm{r}^{2}}\)

→ Force per unit length between two infinitely long current carrying parallel conductors is
F = \(\frac{\mu_{0}}{4 \pi} \cdot \frac{2 \mathrm{I}_{1} \mathrm{I}_{2}}{\mathrm{r}}\)

→ qυB = \(\frac{\mathrm{m} v^{2}}{\mathrm{r}}\) ⇒ r = \(\frac{\mathrm{m} v}{\mathrm{q} \mathrm{B}}\)

→ Time period, T = \(\frac{2 \pi m}{B q}\)

→ \(\overrightarrow{\mathrm{B}}\) due to current carrying conductor is
B = \(\frac{\mu_{0}}{4 \pi}\).\(\frac{\mathrm{Id} l \sin \theta}{\mathrm{r}^{2}}\)
or
\(\overrightarrow{\mathrm{B}}\) = \(\frac{\mu_{0}}{4 \pi} \cdot \frac{\mathrm{I} \overrightarrow{\mathrm{d} l} \times \hat{\mathrm{r}}}{\mathrm{r}^{2}}=\frac{\mu_{0}}{4 \pi} \cdot \frac{\mathrm{I} \overrightarrow{\mathrm{d} l} \times \overrightarrow{\mathrm{r}}}{\mathrm{r}^{3}}\)

→ G.Ig = (I – Ig)S.⇒ S = \(\frac{\mathrm{I}_{\mathrm{g}} \mathrm{G}}{\mathrm{I}-\mathrm{I}_{\mathrm{g}}}\)

→ V = I_g(G + R).

→ R_A = ammeter resistance = \(\frac{\mathrm{GS}}{\mathrm{G}+\mathrm{S}}\)

→ Voltmeter resistance = R_V = G + R

→ No. of revolutions per second = \(\frac{\text { speed }}{\text { circumference }}=\frac{v}{2 \pi r}\)

→ I = ne, where n = \(\frac{\mathrm{v}}{2 \pi \mathrm{r}}\)

→ Force on current carrying conductor in a \(\overrightarrow{\mathrm{B}}\) is, F = BIl sin θ

→ F_max = BIl if θ = 90°.

→ Current sensitivity = \(\frac{\theta}{I}=\frac{N A B}{k}\)

→ Voltage sensitivity = \(\frac{\theta}{\mathrm{V}}=\frac{\theta}{\mathrm{IR}}=\frac{\mathrm{SI}}{\mathrm{R}}=\frac{\mathrm{NAB}}{\mathrm{kR}}\)

→ Torque on a current carrying coil in \(\overrightarrow{\mathrm{B}}\)is τ = nBAI sin θ = nBIA cos α where θ = angle made by \(\overrightarrow{\mathrm{B}}\) with the normal to the plane of coil and
α = angle made by \(\overrightarrow{\mathrm{B}}\) with the plane of coil.