Class 12 Physics

Class 12 Physics Electrostatic Potential and Capacitance Notes

2.1 Introduction

In the previous chapter, we studied electric charges and electric fields. In this chapter, we introduce electrostatic potential, which helps describe electric fields in terms of energy. The concept of capacitance explains how electrical energy can be stored using conductors.

2.2 Electrostatic Potential

Electrostatic potential at a point is defined as the work done per unit positive test charge in bringing it from infinity to that point without acceleration. $V = \frac{W}{q}$ V=qW

SI unit: volt (V)
It is a scalar quantity

2.3 Potential due to a Point Charge

The electrostatic potential due to a point charge q at a distance r is given by: $V = \frac{1}{4\pi\varepsilon_0}\frac{q}{r}$ V=4πε01rq

Potential depends on distance, not direction.
Positive charge produces positive potential; negative charge produces negative potential.

2.4 Potential due to an Electric Dipole

An electric dipole consists of two equal and opposite charges separated by a small distance.

The potential due to a dipole depends on:
- Dipole moment
- Distance from the dipole
- Orientation with respect to the point

On the equatorial line of a dipole, the net potential is zero.

2.5 Potential due to a System of Charges

The total electrostatic potential due to multiple charges is the algebraic sum of potentials due to individual charges. $V_{total} = V_1 + V_2 + V_3 + …$ Vtotal=V1+V2+V3+…

This follows the principle of superposition.

2.6 Equipotential Surfaces

Equipotential surfaces are surfaces on which the electric potential remains constant.

Properties

No work is done in moving a charge along an equipotential surface.
Electric field is always perpendicular to equipotential surfaces.
Closer surfaces indicate stronger electric fields.

2.7 Potential Energy of a System of Charges

The potential energy of a system of charges is the energy required to assemble the system from infinity.

For two point charges:

$U = \frac{1}{4\pi\varepsilon_0}\frac{q_1 q_2}{r}$ U=4πε01rq1q2

Potential energy depends on relative positions of charges.

2.8 Potential Energy in an External Field

When a charge or dipole is placed in an external electric field:

A single charge gains potential energy due to its position.
A dipole experiences potential energy depending on its orientation.

$U = -\vec{p} \cdot \vec{E}$ U=−p⋅E

2.9 Electrostatics of Conductors

Conductors in electrostatic equilibrium have special properties:

Electric field inside a conductor is zero.
Excess charge resides only on the surface.
The surface of a conductor is an equipotential surface.
Electric field is normal to the surface.

2.10 Dielectrics and Polarisation

Dielectrics are insulating materials that become polarised in an electric field.

Polarisation reduces the effective electric field.
Dielectrics increase the capacitance of capacitors.
Examples: Glass, mica, rubber

2.11 Capacitors and Capacitance

A capacitor is a device used to store electric charge.

Capacitance (C): $C = \frac{Q}{V}$ C=VQ

SI unit: farad (F)
Depends on geometry and dielectric medium, not on charge.

2.12 The Parallel Plate Capacitor

A parallel plate capacitor consists of two large parallel conducting plates.

Capacitance: $C = \frac{\varepsilon_0 A}{d}$ C=dε0A

where
A = area of plates
d = separation between plates

2.13 Effect of Dielectric on Capacitance

When a dielectric is inserted between capacitor plates: $C = K \frac{\varepsilon_0 A}{d}$ C=Kdε0A

where K is the dielectric constant.

Capacitance increases by a factor of K.
Electric field inside the capacitor decreases.

2.14 Combination of Capacitors

Capacitors can be connected in:

Series

Same charge on each capacitor
Equivalent capacitance decreases

Parallel

Same potential difference
Equivalent capacitance increases

2.15 Energy Stored in a Capacitor

Energy stored in a charged capacitor is: $U = \frac{1}{2}CV^2$ U=21CV2

Energy is stored in the electric field between plates.
Energy density depends on electric field strength.