By going through these CBSE Class 12 Physics Notes Chapter 2 Electrostatic Potential and Capacitance, students can recall all the concepts quickly.
Electrostatic Potential and Capacitance Notes Class 12 Physics Chapter 2
→ The S.I. unit of electric potential and a potential difference is volt.
→ 1 V = 1 J C-1.
→ Electric potential due to a + ve source charge is + ve and – ve due to a – ve charge.
→ The change in potential per unit distance is called a potential gradient.
→ The electric potential at a point on the equatorial line of an electric dipole is zero.
→ Potential is the same at every point of the equipotential surface.
→ The electric potential of the earth is arbitrarily assumed to be zero.
→ Electric potential is a scalar quantity.
→ The electric potential inside the charged conductor is the same as that on its surface. This is true irrespective of the shape of the conductor.
→ The surface of a charged conductor is equipotential irrespective of its shape.
→ The potential of a conductor varies directly as the charge on it. i.e., V ∝ \(\frac{l}{A}\)
→ Potential varies inversely as the area of the charged conductor i.e.
→ S.I. unit of capacitance is Farad (F).
→ The aspherical capacitor consists of two concentric spheres.
→ A cylindrical capacitor consists of two co-axial cylinders.
→ Series combination is useful when a single capacitor is not able to tolerate a high potential drop.
→ Work done in moving a test charge around a closed path is always zero.
→ The equivalent capacitance of series combination of n capacitors each of capacitance C is
Cs = \(\frac{C}{n}\)
→ Cs is lesser than the least capacitance in the series combination.
→ The parallel combination is useful when we require large capacitance and a large charge is accumulated on the combination.
→ If two charged conductors are connected to each other, then energy is lost due to sharing of charges, unless initially, both the conductors are at the same potentials.
→ The capacitance of the capacitor increases with the dielectric constant of the medium between the plates.
→ The charge on each capacitor remains the same but the potential difference is different when the capacitors are connected in series.
→ P. D. across each capacitor remains the same but the charge stored across each is different during the parallel combination of capacitors.
→ P.E. of the electric dipole is minimum when θ = 0 and maximum when θ = 180°
→ θ = 0° corresponds to the position of stable equilibrium and θ = π to the position of unstable equilibrium.
→ The energy supplied by a battery to a capacitor is CE2 but energy stored
in the capacitor is \(\frac{1}{2}\) CE2.
→ A suitable material for use as a dielectric in a capacitor must have a high dielectric constant and high dielectric strength.
→ Van-de Graaf generator works on the principle of electrostatic. induction and action of sharp points on a charged conductor.
→ The potential difference between the two points is said to be 1 V if 1 J of work is done in moving 1 C test charge from one point to the another.
→ The electric potential at a point in \(\overrightarrow{\mathrm{E}}\): It is defined as the amount of work done in moving a unit + ve test charge front infinity to that point.
→ Electric potential energy: It is defined as the amount of work is done in bringing the charges constituting a system from infinity to their respective locations.
→ 1 Farad: The capacitance of a capacitor is said to be 1 Farad if 1 C charge given to it raises its potential by 1 V
→ Dielectric: It is defined as an insulator that doesn’t conduct electricity but the induced charges are produced on its faces when placed in a uniform electric field.
→ Dielectric Constant: It is defined as the ratio of the capacitance of the capacitor with a medium between the plates to its capacitance with air between the plates
→ Polarisation: It is defined as the induced dipole moment per unit volume of the dielectric slab.
→ The energy density of the parallel plate capacitor is defined as the energy per unit volume of the capacitor.
→ Electrical Capacitance: It is defined as the ability of the conductor to store electric charge.
Important Formulae
→ Electric potential at a point A is
VA = \(\frac{W_{∞} A}{q_{0}}\)
→ V = \(\frac{1}{4 \pi \varepsilon_{0}}. \frac{q}{r}\)
→ Electric field is related to potential gradient as:
E = – \(\frac{\mathrm{dV}}{\mathrm{dr}}\)
→Electric potential at point on the axial line of an electric dipole is:
V = \(\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{q}{r^{2}}\)
→ Electric P.E. of a system of point charges is given
υ = \(\frac{1}{4 \pi \varepsilon_{0}} \sum_{i=1}^{n} \sum_{j=1 \atop j \neq i}^{n} \frac{q_{i} a_{j}}{r_{i j}}\)
→ V due to a charged circular ring on its axis is given by:
V = \(\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{q}{\left(R^{2}+r^{2}\right)^{1 / 2}}\)
→ V at the centre of ring of radius R is given by
V = \(\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{q}{R}\)
→ The work done in moviag a test large from one point A to another point B having positions vectors \(\overrightarrow{\mathrm{r}_{\mathrm{A}}}\) and \(\overrightarrow{\mathrm{r}_{\mathrm{A}}}\) respectively w.r.t. q is given by
WAB = \(\frac{1}{4 \pi \varepsilon_{0}} \cdot q \cdot\left(\frac{1}{r_{B}}-\frac{1}{r_{A}}\right)\)
→ Line integral of electric field between points A and B is given by.
∫AB \(\overrightarrow{\mathrm{E}}\) \(\overrightarrow{\mathrm{dl}}\) = \(\frac{1}{4 \pi \varepsilon_{0}} \cdot \mathrm{q}\left(\frac{1}{\mathrm{r}_{\mathrm{A}}}-\frac{1}{\mathrm{r}_{\mathrm{B}}}\right)\)
→ Electric potential energy of an electric dipole is
U = – \(\overrightarrow{\mathrm{p}}\). \(\overrightarrow{\mathrm{E}}\)
→ Capacitance of the capacitor is given by
C = \(\frac{q}{V}\)
→ P.E. of a charged capacitor is:
U = \(\frac{1}{2}\) qV = \(\frac{1}{2}\) CV2 = \(\frac{\mathrm{q}^{2}}{2 \mathrm{C}}\)
→ C of a parallel plate capacitor with air between the plates is:
C0 = \(\frac{\varepsilon_{0} \cdot A}{d}\)
C0 = \(\frac{\varepsilon_{0} \mathrm{KA}}{\mathrm{d}}\)
→ C of a parallel plate capacitor with a dielectric medium between the plates is:
C = \(\frac{C_{m}}{C_{0}}=\frac{E_{0}}{E}\)
→ Common potential as
V = \(\frac{C_{1} V_{1}+C_{2} V_{2}}{C_{1}+C_{2}}\)
→ loss of electrical energy = \(\frac{1}{2}\left(\frac{\mathrm{C}_{1} \mathrm{C}_{2}}{\mathrm{C}_{1}+\mathrm{C}_{2}}\right)\left(\mathrm{V}_{1}-\mathrm{V}_{2}\right)\)
→ Energy supplied by battery is CE2 and energy stored in the capacitor is \(\frac{1}{2}\) CE2.
→ The equivalent capacitance of series combination of three capacitor is given by
\(\frac{1}{C_{s}}=\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}}\)
→ The equivalent capacitance of parallel grouping of three capacitors is
Cp = C1 + C2 + C3
→ Capacitance of spherical capacitor is
C = 4πε0 \(\frac{a b}{b-a}\)
a, b are radii of inner and outer spheres.
→ Capacitance of a cylindrical capacitor is given by:
C = \(\frac{2 \pi \varepsilon_{0}}{\log _{e}\left(\frac{b}{a}\right)}\)
when b, a are radii of outer and inner cylinder.
→ Capacitance of a capacitor in presence of conducting slab between the plates is .
C = \(\frac{\mathrm{C}_{0}}{1-\frac{\mathrm{t}}{\mathrm{d}}}\) = ∞ if t = d.
→Capacitances of a capacitor with a dielectric medium between the plates is given by
C = \(\frac{C_{0}}{\left[1-\frac{t}{d}\left(1-\frac{1}{R}\right)\right]}\)
C = K C0 If t = d
→ Reduced value of electric field in a dielectric slab is given by
E = E0 – \(\frac{P}{\varepsilon_{0}}\)
where P = σp = induced charge density.
→ Capacitance of an isolated sphere is given by
C = 4πε0 r .
C = 4πε0 Kr