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

C_{s} = \(\frac{C}{n}\)

→ C_{s} 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 CE^{2} but energy stored

in the capacitor is \(\frac{1}{2}\) CE^{2}.

→ 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

V_{A} = \(\frac{W_{∞} A}{q_{0}}\)

→ 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 = \(\frac{1}{2}\) CV^{2} = \(\frac{\mathrm{q}^{2}}{2 \mathrm{C}}\)

→ C of a parallel plate capacitor with air between the plates is:

C_{0} = \(\frac{\varepsilon_{0} \cdot A}{d}\)

C_{0} = \(\frac{\varepsilon_{0} \mathrm{KA}}{\mathrm{d}}\)

→ 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 \(\frac{1}{2}\) CE^{2}.

→ 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

C_{p} = C_{1} + C_{2} + C_{3}

→ Capacitance of spherical capacitor is

C = 4πε_{0} \(\frac{a b}{b-a}\)

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 C_{0} If t = d

→ Reduced value of electric field in a dielectric slab is given by

E = E_{0} – \(\frac{P}{\varepsilon_{0}}\)

where P = σ_{p} = induced charge density.

→ Capacitance of an isolated sphere is given by

C = 4πε_{0} r .

C = 4πε_{0} Kr