Electric Field in Conductors: JEE Main Guide

The behaviour of conductors in electrostatic equilibrium is one of the most conceptually elegant topics in JEE Main Physics. Three statements — field is zero inside, field is perpendicular to the surface outside, and all charge resides on the surface — follow rigorously from Gauss's law and form the basis of multiple JEE Main questions per year. This guide covers these ideas completely, including the cavity theorem and electrostatic shielding.

Electrostatic Equilibrium: The Three Facts

Fact 1: Electric field inside a conductor in electrostatic equilibrium is zero. Reason: if E ≠ 0 inside, free electrons would experience a force and move, contradicting "equilibrium." The electrons redistribute until their field exactly cancels any external field inside. Fact 2: Any excess charge resides entirely on the outer surface (or inner surface if a cavity with charge is present). Proven by applying Gauss's law to a surface just inside the conductor surface — since E = 0 inside, the enclosed charge must be zero. Fact 3: The electric field at the conductor surface is perpendicular to the surface. If there were a component parallel to the surface, surface charges would move — again contradicting equilibrium. For Gauss's law applications, see our Gauss's Law Guide.

Surface Charge Density and Electric Field

Just outside a conductor surface: E = σ/ε₀, directed perpendicular to the surface. The charge distributes non-uniformly on an irregular conductor — higher density at sharp points (smaller radius of curvature), lower density on flat surfaces. This is why lightning rods are pointed: the high local field at the tip initiates corona discharge. JEE Main asks: given charge Q on a conductor of known geometry, find the surface charge density at a specified point. For irregular geometries, the result is qualitative (higher at sharper regions). Take a free mock test on electrostatics including conductor problems to practise these concepts.

Cavity Inside a Conductor: The Shell Theorem

Case 1: Conductor with a cavity, no charge inside cavity. By Gauss's law applied to a surface inside the conductor enclosing the cavity: since E = 0 on this surface, Q_enclosed = 0. The inner surface of the cavity has zero charge. The cavity field is zero — perfect electrostatic shielding (Faraday cage). This is why the inside of a car is safe during a lightning storm (the metal body shields the interior).

Case 2: Conductor with a cavity containing a charge +Q. The inner surface of the cavity acquires induced charge −Q (by Gauss's law — the induced charge creates zero field inside the conductor). The outer surface acquires charge +Q (charge conservation on the conductor). The electric field inside the conductor remains zero, and the field outside the conductor corresponds to +Q on the outer surface. JEE Main tests this two-surface charge distribution in problems involving nested conductors.

Earthing (Grounding) a Conductor

Earthing (connecting a conductor to ground) allows charge to flow to or from the Earth until the conductor reaches zero potential. JEE Main uses earthing in the context of two conductors: a charged sphere A near an earthed sphere B. The earthed sphere acquires an induced charge that brings its potential to zero. The charge on B is found by setting V_B = 0 using the superposition of potentials from A's charge and B's own induced charge. This calculation is a standard JEE Main problem type.

Charge Redistribution Between Two Conductors

Two isolated spherical conductors (radii r₁ and r₂, charges Q₁ and Q₂) are connected by a conducting wire: charge redistributes until they reach the same potential. Final charges Q₁' and Q₂': Q₁'/r₁ = Q₂'/r₂ (potential equal) and Q₁' + Q₂' = Q₁ + Q₂ (charge conservation). Solving: Q₁' = r₁(Q₁+Q₂)/(r₁+r₂). Energy is lost during redistribution (heat in the wire). JEE Main tests both the final charge distribution and the energy lost.

Exam Strategy

Conductor questions in JEE Main are mostly conceptual or require applying the three fundamental facts plus Gauss's law. The cavity problem (charge Q inside → −Q on inner surface, +Q on outer surface) is the most-tested specific scenario. Practise stating the three conductor facts from memory — students who cannot instantly recall "field is zero inside" make errors on every conductor question. For the complete electrostatics framework, see our Electrostatics Complete Guide. Upgrade for ₹149/month for 150+ conductor and Gauss's law problems.