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