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Class 12 Physics: Electrostatic Potential and Capacitance

This lecture covers electric potential, potential difference, potential due to a point charge and electric dipole, equipotential surfaces, and electrostatic shielding. It also explains capacitor principles, capacitance of isolated and parallel plate conductors, energy stored, energy density, and dielectric effects.

Class 12 Science
JEE
NEET
Physics
English
· 10 topics
Checked against the video on 19 Oct 2026

Made by AI from the YouTube video Electrostatic Potential And Capacitance Class 12 | Physics Chapter 2 | Revision | Shailendra Sir (opens YouTube in a new tab) by NCERT Wallah, then checked against it. All credit for the teaching goes to the creator. Tap a topic’s time to confirm a fact in the video.

Class 12 Physics: Electrostatic Potential and Capacitance

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This lecture covers electric potential, potential difference, potential due to a point charge and electric dipole, equipotential surfaces, and electrostatic shielding. It also explains capacitor principles, capacitance of isolated and parallel plate conductors, energy stored, energy density, and dielectric effects.

Potential Difference and Electric Potential

Potential difference between two points in an electrostatic field is defined as the work done in moving a unit positive charge from one point to another against electrostatic forces.
The formula for potential difference between points A and B is VB - VA = W_AB / q0, where q0 is the positive test charge.
Potential difference and electric potential are scalar quantities having the SI unit of Volt (V) or Joule per Coulomb (J/C).
Electric potential at a point is the work done per unit test charge in bringing it from infinity to that point against electrostatic forces: V_P = W_infinity->P / q0.
Must knowThe electrostatic potential at infinity is taken to be zero.

Electric Potential Due to a Point Charge

Electrostatic force acting on a test charge q0 located at distance x from source charge q is given by Coulomb's law: F = (1 / (4πε0)) × (q × q0 / x²).
The elementary work done for a displacement dx against the electrostatic repulsive force is dW = -F dx.
Integrating dW from infinity to r yields the total work done: W = (1 / (4πε0)) × (q × q0 / r).
Must knowThe electric potential V at distance r from a point charge q is V = (1 / (4πε0)) × (q / r).
The work done in moving a charge in an electrostatic field is path-independent because electrostatic forces are conservative forces.

Potential Gradient and Electric Field Relation

Potential gradient is defined as the rate of change of electric potential with respect to distance (-dV/dx).
Must knowThe relation between electric field and potential gradient is E = -dV/dx.
Electric field lines always point in the direction of decreasing electric potential, meaning electric field flows from high potential to low potential.
In a direction perpendicular to the electric field lines, the electric potential remains constant.

Potential Due to an Electric Dipole

For an electric dipole consisting of charges -q and +q separated by 2l, the potential at an axial point distance r from the centre is V_axial = (1 / (4πε0)) × (p / (r² - l²)), which simplifies to (1 / (4πε0)) × (p / r²) for r >> l.
Along the axial line, the dipole potential varies inversely with the square of distance: V ∝ 1/r².
Must knowThe electric potential at any point on the equatorial line (perpendicular bisector) of an electric dipole is identically zero.
At any general point (r, θ) from the dipole centre, the potential is given by V = (1 / (4πε0)) × (p cosθ / r²).

Capacitance and Coalescing Drops

Electric potential of a spherical drop of radius r carrying charge q is given by V = (1 / (4πε0)) × (q / r).
When 27 identical small spherical drops coalesce into a single larger drop, total volume remains conserved: (4/3)πR³ = 27 × (4/3)πr³, giving R = 3r.
Total charge on the combined drop is 27 times the individual charge: Q = 27q.
Must knowThe potential of the combined drop becomes V' = 9 × V, yielding 1980 V when the potential of each small drop is 220 V.

Equipotential Surfaces and Electrostatic Shielding

An equipotential surface is any surface that has the same electric potential at every point on it.
Work done in moving any charge between two points on an equipotential surface is always zero (W = q ΔV = 0).
Electric field lines are always normal (perpendicular) to the equipotential surface at every point.
Equipotential surfaces are closer together in regions of strong electric fields and farther apart in weak electric fields.
Must knowTwo equipotential surfaces can never intersect each other because that would imply two different potentials at the point of intersection.
Inside the cavity of a hollow conductor, the electric field vanishes completely, an effect called electrostatic shielding.

Potential Energy of Charges and Dipole

Electrostatic potential energy of two point charges q1 and q2 separated by distance r is U = (1 / (4πε0)) × (q1 × q2 / r).
For a system of three point charges, the total potential energy is the sum of interaction energies of all pairs: U = (1 / (4πε0)) × [(q1 q2 / r12) + (q1 q3 / r13) + (q2 q3 / r23)].
Work done to rotate an electric dipole in a uniform electric field from θ1 to θ2 is W = pE (cosθ1 - cosθ2).
Potential energy stored in a dipole oriented at angle θ in a uniform electric field is U = -pE cosθ = -p · E.
Must knowStable equilibrium of a dipole occurs when θ = 0° (minimum potential energy, U = -pE), while unstable equilibrium occurs when θ = 180° (maximum potential energy, U = +pE).

Capacitance of a Conductor and Parallel Plate Capacitor

Charge given to an isolated conductor is directly proportional to its potential: q = CV, where C is capacitance.
Capacitance depends on the size, shape, and surrounding medium of the conductor, and is independent of q and V.
Capacitance of an isolated spherical conductor of radius R in vacuum is C = 4πε0 R; in a dielectric medium of constant K, it becomes C' = 4πε0 K R.
Must knowCapacitance of a parallel plate capacitor with plate area A and separation d in vacuum is C = ε0 A / d.
Inserting a dielectric of constant K between the plates increases the capacitance to C' = K C = K ε0 A / d.

Energy Stored and Redistribution of Charges

Electrostatic energy stored in a charged capacitor or conductor is given by U = (1/2) CV² = (1/2) qV = q² / (2C).
Energy density of an electric field between capacitor plates is u = (1/2) ε0 E².
When two charged conductors are connected, charge flows from higher potential to lower potential until they reach a common potential: V = (C1 V1 + C2 V2) / (C1 + C2).
Charge transferred from the first conductor is Δq = [C1 C2 / (C1 + C2)] × (V1 - V2).
Must knowConnecting two charged conductors always results in an energy loss dissipated as heat: ΔU = [C1 C2 / (2(C1 + C2))] × (V1 - V2)².

Dielectrics, Polarization, and Susceptibility

When a dielectric slab is placed in an external electric field E0, charges are induced on its surfaces, creating an internal opposing electric field Ei.
The net electric field inside the dielectric is reduced: E_net = E0 - Ei = E0 / K.
Induced charge on the dielectric faces is given by q_i = q (1 - 1/K).
Polarization density P is the induced dipole moment per unit volume, which equals the induced surface charge density: P = σ_p.
Electric susceptibility χ relates polarization to net field: P = ε0 χ E.
Must knowThe dielectric constant K and electrical susceptibility χ are related by K = 1 + χ.

Key terms

Electric Potential: Work done per unit test charge in bringing it from infinity to a given point against electrostatic forces.
Potential Gradient: The spatial rate of change of potential with distance (-dV/dx), equal in magnitude and opposite in sign to the electric field.
Equipotential Surface: A surface having the identical electrostatic potential at every point on it.
Electrostatic Shielding: The phenomenon of protecting a region from external electric fields by enclosing it inside a hollow metallic conductor.
Capacitance: The ability of a conductor or system of conductors to store electric charge and electrical energy per unit potential.
Dielectric Breakdown: The phenomenon where an insulating dielectric material becomes conducting when subjected to an excessively high electric field.
Electric Susceptibility (χ): A dimensionless proportionality constant linking the polarization density of a dielectric to the applied electric field: P = ε0 χ E.

Formulas

V = (1 / (4πε0)) × (q / r): Electric potential at distance r from a point charge
E = -dV/dx: Relation between electric field and potential gradient
V_dipole = (1 / (4πε0)) × (p cosθ / r²): Electric potential due to a short dipole at (r, θ)
W = pE (cosθ1 - cosθ2): Work done in rotating a dipole in a uniform electric field
U = -p · E = -pE cosθ: Potential energy of an electric dipole in a uniform electric field
C = ε0 A / d: Capacitance of a parallel plate capacitor in vacuum
C = 4πε0 R: Capacitance of an isolated spherical conductor of radius R
U = (1/2) CV² = (1/2) qV = q² / (2C): Electrostatic energy stored in a capacitor
u = (1/2) ε0 E²: Energy density of an electric field in vacuum
V_common = (C1 V1 + C2 V2) / (C1 + C2): Common potential of two connected conductors
ΔU = [C1 C2 / (2(C1 + C2))] × (V1 - V2)²: Loss of electrostatic energy on sharing charges
q_i = q (1 - 1/K): Induced charge on dielectric faces
K = 1 + χ: Relation between dielectric constant and electric susceptibility

Quick revision

The electric potential at infinity is taken as zero.
Electrostatic force is conservative, making work done path-independent.
Electric field always points in the direction of decreasing potential.
The electric potential on the equatorial plane of an electric dipole is zero at all points.
No work is done in moving any charge along an equipotential surface.
Inside a hollow charged conductor, the electric field is zero and potential remains constant and equal to surface potential.
Stable equilibrium of an electric dipole occurs at θ = 0° with potential energy U = -pE.
Unstable equilibrium of an electric dipole occurs at θ = 180° with potential energy U = +pE.
Connecting two charged conductors always causes a loss of energy given by [C1 C2 / (2(C1 + C2))] × (V1 - V2)².
Placing a dielectric of constant K between capacitor plates increases capacitance by a factor of K.

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