CBSE Class 12 Physics – Chapter 2: Electrostatic
Potential and Capacitance
1. Electrostatic Potential
Definition: Work done per unit positive test charge to move it from infinity to a point
in an electric field.
V=WqV = \frac{W}{q}V=qW
Unit: Volt (V) = Joule/Coulomb.
Potential due to a point charge:
V=14πϵ0⋅qrV = \frac{1}{4\pi\epsilon_0} \cdot \frac{q}{r}V=4πϵ01⋅rq
Potential due to multiple charges: Algebraic sum of individual potentials.
Potential due to an electric dipole:
V=14πϵ0⋅pcosθr2V = \frac{1}{4\pi\epsilon_0} \cdot \frac{p\cos\theta}{r^2}V=4πϵ01
⋅r2pcosθ
2. Equipotential Surfaces
Surfaces where potential is constant.
No work is done when moving a charge along an equipotential surface.
Electric field is always perpendicular to equipotential surfaces.
3. Relation Between Electric Field and Potential
E =−∇V\vec{E} = -\nabla VE=−∇V
In one dimension:
Ex=−dVdxE_x = -\frac{dV}{dx}Ex=−dxdV
4. Potential Energy of a System of Charges
Two charges:
U=14πϵ0⋅q1q2rU = \frac{1}{4\pi\epsilon_0} \cdot \frac{q_1 q_2}{r}U=4πϵ01⋅rq1q2
Electric dipole in a uniform field:
U=−p ⋅E =−pEcosθU = -\vec{p} \cdot \vec{E} = -pE\cos\thetaU=−p⋅E=−pEcosθ
