Chapter 2 — Electrostatic Potential and Capacitance

Chapter 2 of the Class 12 Physics NCERT textbook, "Electrostatic Potential and Capacitance", covers electrostatic potential and capacitance, explaining how electric potential is the work done per unit positive charge in bringing it from infinity to a point, and how capacitors store energy using the relation C = Q/V.

• Potential as stored electrical work — The chapter reframes electric interactions in terms of energy: potential is the work needed to bring a unit charge from infinity to a point, giving a scalar tool that is often simpler to use than the vector field.
• Equipotentials and conductors — Surfaces of constant potential run perpendicular to the field, and conductors are explored as special equipotential bodies — field-free inside, with charge on the outer surface, explaining electrostatic shielding.
• Capacitors as charge stores — A capacitor's ability to hold charge depends only on its geometry, and inserting a dielectric boosts this capacity. This principle underlies how devices store electrical energy for later use.
• Energy in the electric field — Building on capacitance, the chapter shows energy can be viewed as residing in the field itself, quantified through the energy stored in a capacitor and the field's energy density.

1. 01Electrostatic potential at a point equals the work done by an external force per unit positive charge in bringing it from infinity to that point, with potential at infinity taken as zero.
2. 02Potential due to a point charge Q at distance r is V = Q/(4πε₀r); for a dipole it falls off as 1/r² and depends on the angle with the dipole moment.
3. 03Equipotential surfaces are always perpendicular to the electric field; no work is done moving a charge along an equipotential surface.
4. 04Inside a conductor the electric field is zero, potential is constant throughout, and any excess charge resides only on the outer surface (electrostatic shielding applies to cavities).
5. 05Capacitance C = Q/V depends only on geometry; for a parallel plate capacitor C = ε₀A/d, and inserting a dielectric of constant K increases it to C = Kε₀A/d.
6. 06Energy stored in a capacitor is U = Q²/(2C) = (1/2)CV² = (1/2)QV, and the energy density of an electric field is u = (1/2)ε₀E².