CBSE Class 12 Physics Revision Notes Chapter 2: Electrostatic Potential and Capacitance

Electrostatic potential is the work done per unit positive charge in bringing it from infinity to a point in an electric field. For CBSE Class 12 Physics, the chapter connects potential, conductors, dielectrics, capacitance and electrical energy storage.

Electrostatic Potential and Capacitance explains how work and energy are associated with stationary electric charges. It introduces potential due to point charges, dipoles and systems of charges. It also explains how capacitors store charge and energy.

Use these CBSE Class 12 Physics Revision Notes Chapter 2 for the 2026–27 session. Revise definitions first, followed by formulas, conductor properties, dielectrics, capacitor combinations and stored energy.

Key Takeaways

• Electrostatic potential: Work done per unit positive test charge in bringing it from infinity to a point.
• Equipotential surface: The potential remains constant, so no work is done along the surface.
• Capacitance: C = Q/V, and its SI unit is farad.
• Stored energy: U = ½CV² = ½QV = Q²/2C.

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Electrostatic Potential and Potential Difference Class 12 Physics Notes

Electrostatic force is a conservative force. Therefore, work done between two points depends on the initial and final positions, not the path followed.

Electrostatic Potential Energy

Electrostatic potential energy is the energy stored when a charge is moved against an electrostatic force.

The change in potential energy is equal to the work done by an external force:

ΔU = UP − UR = WRP

Only the difference in potential energy has physical significance. Its zero can be selected at any convenient point, usually infinity.

Electrostatic Potential

Electrostatic potential at a point is the work done by an external force in bringing a unit positive test charge from infinity to that point.

V = W/q

Here:

• V is electrostatic potential.
• W is the external work done.
• q is the test charge.

Electrostatic potential is a scalar quantity. Its SI unit is volt.

1 V = 1 J/C

Potential Difference and Work Done

Potential difference between points A and B is the work done per unit positive charge in moving it from A to B.

VB − VA = WAB/q

The work done in moving charge q through a potential difference is:

WAB = q(VB − VA)

Potential difference is physically significant. The actual potential depends on the selected zero-potential reference.

Potential Due to Different Charge Configurations in Chapter 2 Notes

Potential follows the superposition principle. The total potential equals the algebraic sum of potentials due to individual charges.

Potential Due to a Point Charge

For a point charge Q, potential at a distance r is:

V = 1/(4πε₀) × Q/r

or

V = kQ/r

where:

k = 1/(4πε₀)

Important points:

• V is positive for a positive charge.
• V is negative for a negative charge.
• V varies as 1/r.
• Potential at infinity is taken as zero.

The electric field of a point charge varies as 1/r², while its potential varies as 1/r.

Potential Due to an Electric Dipole

An electric dipole consists of charges +q and −q separated by distance 2a.

Its dipole moment is:

p = q(2a)

The direction of p is from the negative charge to the positive charge.

At a distant point:

V = 1/(4πε₀) × p cos θ/r²

This expression applies when r is much greater than a.

On the dipole axis:

θ = 0° or 180°

V = ±1/(4πε₀) × p/r²

On the equatorial plane:

θ = 90°

V = 0

The dipole potential depends on both distance r and angle θ. It decreases as 1/r² at large distances.

Potential Due to a System of Charges

For charges q₁, q₂, q₃, …, qₙ, the potential at point P is:

V = 1/(4πε₀) × (q₁/r₁ + q₂/r₂ + q₃/r₃ + … + qₙ/rₙ)

Potential is added algebraically because it is a scalar quantity. The signs of all charges must be included.

Potential Due to a Uniformly Charged Spherical Shell

Let a spherical shell of radius R carry total charge Q.

Outside the shell, where r ≥ R:

V = 1/(4πε₀) × Q/r

The shell behaves as if its entire charge were concentrated at its centre.

On the surface:

V = 1/(4πε₀) × Q/R

Inside the shell, where r < R:

V = 1/(4πε₀) × Q/R

The potential remains constant throughout the interior. However, the electric field inside the shell is zero.

Equipotential Surfaces and Electric Field Potential Relation Notes

An equipotential surface has the same potential at every point. Moving a charge along such a surface requires no work.

Properties of Equipotential Surfaces

• Potential remains constant at every point.
• Work done in moving a charge along the surface is zero.
• Electric field is always perpendicular to the surface.
• Two equipotential surfaces cannot intersect.
• Closely spaced surfaces represent a stronger electric field.
• Widely spaced surfaces represent a weaker electric field.

For a point charge, equipotential surfaces are concentric spheres centred on the charge.

For a uniform electric field, equipotential surfaces are parallel planes perpendicular to the field.

Relation Between Electric Field and Potential

Electric field points in the direction of the steepest decrease in potential.

For a small displacement dl along the field:

E = −dV/dl

In one dimension:

Ex = −dV/dx

The negative sign shows that potential decreases in the direction of the electric field.

For a uniform electric field:

VB − VA = −E·d

If displacement d is along the electric field:

VB − VA = −Ed

Electrostatic Potential Energy Class 12 Physics Chapter 2 Notes

Potential energy represents the work required to assemble a charge configuration.

Potential Energy of a System of Charges

For two point charges q₁ and q₂ separated by distance r₁₂:

U = 1/(4πε₀) × q₁q₂/r₁₂

For three charges:

U = 1/(4πε₀) × (q₁q₂/r₁₂ + q₂q₃/r₂₃ + q₃q₁/r₃₁)

For a system of several charges, include the interaction energy of every distinct pair once.

• U is positive for like charges.
• U is negative for unlike charges.
• The reference value is generally taken as zero when all charges are infinitely separated.

Potential Energy in an External Field

If a charge q is placed at a point where the external potential is V(r), its potential energy is:

U = qV(r)

The potential V(r) must be due to external charges. It must not include the potential created by charge q itself.

Potential Energy of an Electric Dipole

For an electric dipole of moment p placed in a uniform electric field E:

U = −p·E

U = −pE cos θ

The dipole has minimum energy when aligned with the electric field.

Electrostatics of Conductors Revision Notes

A conductor contains free charges. These charges rearrange until electrostatic equilibrium is reached.

Properties of Conductors in Electrostatic Equilibrium

1. Electric field inside a conductor is zero.
   E = 0
2. Potential is constant throughout the conductor.
   Every point inside and on its surface has the same potential.
3. Excess charge remains on the surface.
   No excess charge remains inside the conducting material.
4. Electric field is normal to the surface.
   A tangential component would move free charges and disturb equilibrium.
5. Field just outside a charged conductor is:
   E = σ/ε₀
   Here, σ is the surface charge density.
6. Charge density is greater at sharper points.
   Charges accumulate more strongly where the radius of curvature is small.

Electrostatic Shielding

A cavity inside a conductor remains protected from external electrostatic fields when no charge is present inside it.

The electric field inside such a cavity is zero. This effect is called electrostatic shielding.

A closed conducting enclosure can therefore protect sensitive equipment from external electric fields.

Dielectrics and Polarisation Class 12 Physics Notes

A dielectric is an insulating material that does not contain free charge carriers. Its molecules become polarised in an external electric field.

Polar and Non-polar Molecules

In an external field, polar molecules tend to align with the field. Non-polar molecules develop an induced dipole moment.

Polarisation and Dielectric Constant

Polarisation P is the dipole moment per unit volume of a dielectric.

When a dielectric is placed in an electric field, an opposing field develops inside it. This reduces the net electric field.

The dielectric constant is:

K = E₀/E

It can also be written as:

K = C/C₀

Therefore:

C = KC₀

Here:

• C₀ is capacitance without the dielectric.
• C is capacitance with the dielectric.
• K is the dielectric constant.

Capacitors and Capacitance Class 12 Chapter 2 Notes

A capacitor consists of two conductors separated by an insulator. The conductors carry equal and opposite charges +Q and −Q.

Capacitance and Its SI Unit

Capacitance is the ratio of charge on either conductor to the potential difference between them.

C = Q/V

Capacitance depends on:

• Shape of the conductors
• Size of the conductors
• Separation between the conductors
• Nature of the medium between them

It does not depend directly on Q or V.

The SI unit of capacitance is farad.

1 F = 1 C/V

Common smaller units are:

• 1 μF = 10⁻⁶ F
• 1 nF = 10⁻⁹ F
• 1 pF = 10⁻¹² F

Parallel-Plate Capacitor

A parallel plate capacitor has two large conducting plates of area A separated by distance d.

For plates carrying surface charge densities +σ and −σ:

E = σ/ε₀

Since:

σ = Q/A

Therefore:

E = Q/(ε₀A)

The potential difference is:

V = Ed

V = Qd/(ε₀A)

Using C = Q/V:

C = ε₀A/d

This expression assumes that the separation is much smaller than the dimensions of the plates. Edge effects are then neglected.

Effect of a Dielectric on Capacitance

When a dielectric of constant K completely fills the space between the plates:

C = Kε₀A/d

Therefore:

C = KC₀

A dielectric increases capacitance by reducing the effective electric field and potential difference for the same charge.

Combination of Capacitors in Class 12 Physics Revision Notes

Capacitors can be connected in series or parallel to obtain a required equivalent capacitance.

Capacitors in Series

In a series combination:

• Each capacitor carries the same charge.
• The total potential difference equals the sum of individual potential differences.
• Equivalent capacitance is less than the smallest individual capacitance.

V = V₁ + V₂ + V₃ + …

Since V = Q/C:

1/Ceq = 1/C₁ + 1/C₂ + 1/C₃ + …

For two capacitors:

Ceq = C₁C₂/(C₁ + C₂)

For n identical capacitors of capacitance C:

Ceq = C/n

Capacitors in Parallel

In a parallel combination:

• Potential difference is the same across every capacitor.
• Total charge equals the sum of individual charges.
• Equivalent capacitance is greater than every individual capacitance.

Q = Q₁ + Q₂ + Q₃ + …

Since Q = CV:

Ceq = C₁ + C₂ + C₃ + …

For n identical capacitors:

Ceq = nC

Series and Parallel Comparison

Energy Stored in a Capacitor Chapter 2 Notes

Charging a capacitor requires work. This work becomes electrostatic potential energy stored in the electric field.

Work Done in Charging a Capacitor

At an intermediate charge q:

V = q/C

The small work required to add charge dq is:

dW = Vdq

dW = qdq/C

Integrating from 0 to Q:

U = Q²/2C

Using Q = CV:

U = ½QV

U = ½CV²

Thus:

U = ½CV² = ½QV = Q²/2C

Energy Density of an Electric Field

For a parallel plate capacitor:

U = ½CV²

Using C = ε₀A/d and V = Ed:

U = ½ε₀E²(Ad)

Here, Ad is the volume between the plates.

Therefore, energy per unit volume is:

u = ½ε₀E²

In a dielectric medium:

u = ½εE²

Battery-Connected and Battery-Disconnected Cases

A dielectric changes the capacitor differently depending on whether the battery remains connected.

For the connected case, the battery supplies additional charge.

For the disconnected case, no additional charge can enter or leave the capacitor.

Electrostatic Potential and Capacitance Formula Notes

Important Terms in Class 12 Physics Chapter 2

Revise Class 12 Physics Chapter 2 Notes in 30 Minutes

A 30-minute revision can be divided into three parts:

• First 10 minutes: Potential, potential difference and charge configurations
• Next 10 minutes: Equipotential surfaces, conductors and dielectrics
• Final 10 minutes: Capacitor combinations, stored energy and formulas

Keep the sign of charges, the selected zero of potential and the battery connection in mind while solving numericals.

Useful Links for Class 12 Physics