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 metre^{2} (Am^{2}).

→ 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 θ_{1 }to θ_{2} is

W = MB (cos θ_{1} – cos θ_{2})

→ 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 = μ_{0} (H + I)

→ B in vacuum is given by

B = μ_{0}H

→ μ = \(\frac{B}{H}\)

→ χ_{m} = \(\frac{I}{H}\)

→ μ = (1 + χ_{m})

or

μ = μ_{0}(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 M_{1} and M_{2} 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 T_{2}

T_{1} = 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 = μ_{0} μ_{r} n I

where n = no. of turns per unit length.

I = current in the ring.