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Conductor questions in electrostatics rarely need heavy calculation. They need you to apply five rules precisely. Students lose marks by putting charge inside a metal, by assuming charge spreads evenly over any shape or by forgetting induced charges on a cavity wall. This post states the rules, works three problems and ends with a practice set.
What are the rules for a conductor in electrostatic equilibrium?
NCERT's Electrostatic Potential and Capacitance chapter lists them. Each follows from one fact: free electrons move whenever there is a field, so in the static state they have arranged themselves to cancel it.
The electrostatic field inside a conductor is zero.
At the surface the field is normal to the surface. Any sideways part would push surface charges along.
The interior has no excess charge. By Gauss's law, any small volume inside has zero flux through its surface, so encloses no net charge. Excess charge lives on the surface.
The potential is the same throughout the conductor and on its surface.
Just outside, E = σ/ε₀, where σ is the local surface charge density.
Conductors in electrostatics appear in the JEE (Main) 2026 and NEET (UG) 2026 syllabi, and the CBSE 2026-27 curriculum lists "free charges and bound charges inside a conductor". Check the current year's documents.
What is electrostatic shielding?
NCERT states a striking result: in a conductor with a cavity containing no charge, the field inside the cavity is zero, whatever the size and shape of the cavity and whatever the charge on the conductor or the outside field. This is electrostatic shielding, used to protect sensitive instruments.
A related everyday example: the US National Weather Service notes that the outer metal shell of a hard-topped car protects people inside with the windows closed, and that rubber tyres do not. Lightning is a current, not a static charge, so this is not strictly electrostatics, but the idea is similar: the charge travels over the outer metal and down to the ground rather than through the space inside.
Example 1: a charge inside a metal shell
A point charge +5.0 nC sits at the centre of a neutral metal shell with inner radius 10 cm and outer radius 12 cm. Find the charge on each surface and the field at 20 cm from the centre. Take k = 9.0 × 10⁹ N m²/C².
Field in the metal is zero, so a Gaussian sphere inside the metal encloses zero net charge. The inner surface must carry −5.0 nC.
The shell is neutral, so the outer surface carries +5.0 nC.
Outside, the field is as if all the enclosed charge (+5.0 − 5.0 + 5.0 = +5.0 nC) were at the centre: E = kq/r² = 9.0 × 10⁹ × 5.0 × 10⁻⁹ / 0.20² = 45/0.04 = 1125 N/C.
Move the charge off-centre and the inner charge redistributes unevenly, but the outer +5.0 nC on a spherical surface stays uniform and the outside field is unchanged. If the outer surface is earthed, its +5.0 nC flows away and the field outside drops to zero: the shield now works in both directions.
Example 2: why do sharp points carry more charge?
Two metal spheres of radius 10 cm and 5.0 cm, far apart, are joined by a thin wire. A total charge of 30 nC is shared between them. Find each charge, potential and surface field.
Connected conductors reach the same potential: kQ₁/R₁ = kQ₂/R₂, so Q₁/Q₂ = R₁/R₂ = 2.
Q₁ = 20 nC, Q₂ = 10 nC.
Potential: V = 9.0 × 10⁹ × 20 × 10⁻⁹ / 0.10 = 1800 V, and 9.0 × 10⁹ × 10 × 10⁻⁹ / 0.050 = 1800 V. Same, as it should be.
Surface field kQ/R²: large sphere 9.0 × 10⁹ × 20 × 10⁻⁹ / 0.010 = 18,000 N/C; small sphere 9.0 × 10⁹ × 10 × 10⁻⁹ / 0.0025 = 36,000 N/C.
The smaller sphere has less charge but twice the surface charge density and twice the field. A sharp point behaves like a very small sphere, which is why charge leaks from points and lightning conductors are pointed.
Example 3: a conductor that is not a sphere
On a charged pear-shaped conductor, where is σ largest? At the most curved end, by the same reasoning as Example 2. The potential is the same everywhere on it, but the charge density and field are not. The equipotential rule is about V, not σ.
Common mistakes
Putting charge inside the metal. Excess charge is on the surfaces only.
Forgetting induced charge on the cavity wall when a charge is placed in the cavity.
Assuming σ is uniform on any shape. Only an isolated sphere has uniform σ.
Thinking the field is zero just outside. Inside is zero; just outside it is σ/ε₀.
Confusing equal potential with equal charge for connected conductors.
For Gaussian surfaces in general, see Gauss's law problems, and for sign and superposition slips, common electrostatics mistakes.
Practice routine
Write the five rules from memory, each with a one-line reason.
Solve three shell problems: charge at centre, charge off-centre, and outer surface earthed.
Solve two connected-sphere problems with different radius ratios, finding Q, V and E for each.
Field lines around conductors are easier to see than to imagine. The Fermi Simulation Lab has interactive simulations for ideas easier to see than read, so you can check where field lines meet a surface at right angles.
Start by redoing Example 2 with radii of 9 cm and 3 cm and a total of 40 nC.
