Questions: Conductors in Electrostatic Equilibrium

Question 1

A conducting sphere carries a net positive charge. Where does this charge reside when the conductor is in electrostatic equilibrium?

• A. Uniformly distributed throughout the interior of the sphere
• B. Concentrated at the geometric center of the sphere
• C. Entirely on the outer surface of the sphere
• D. Half in the interior and half on the surface

Answer: (C)

In electrostatic equilibrium, E = 0 everywhere inside the conductor. By Gauss's law, if E = 0 on every closed surface drawn inside the conductor, the total enclosed charge must be zero. This means no charge can reside in the interior — all excess charge migrates to and stays on the outer surface. This is true regardless of the conductor's shape or the amount of charge.

Question 2

A hollow conducting shell has a point charge +q placed inside its cavity. What is the electric field inside the bulk conducting material of the shell (not inside the cavity)?

• A. Non-zero, pointing away from the central charge
• B. Zero — in electrostatic equilibrium, E = 0 inside any conductor's bulk material
• C. Equal to kq/r² at every point within the conducting material
• D. Non-zero near the inner surface, zero near the outer surface

Answer: (B)

The electric field inside the bulk conducting material is always exactly zero in electrostatic equilibrium, regardless of what charges are present in the cavity or outside. Free charges in the conductor redistribute in response to the interior charge: −q is induced on the inner surface and +q appears on the outer surface. Within the bulk material itself, these rearrangements ensure E = 0. This is the Faraday cage effect.

Question 3

The electric field at the surface of a conductor in electrostatic equilibrium is always perpendicular to the surface.

• T. True
• F. False

Answer: True

If the field had a component tangential to the surface, that component would exert a force on free surface charges and drive a current along the surface — contradicting electrostatic equilibrium. At equilibrium, no currents flow, which requires the tangential component to be zero. Therefore, the field is purely perpendicular (normal) to the conductor's surface, with magnitude σ/ε₀.

Question 4

Charge distributes uniformly over the surface of any conductor in electrostatic equilibrium.

• T. True
• F. False

Answer: False

Uniform surface charge density occurs only for a perfectly spherical conductor. For an irregular conductor, charge concentrates where surface curvature is greatest — especially at sharp points or edges. The external electric field is therefore strongest near tips (σ is highest there). This is why lightning rods use sharp points: intense local fields ionize air, allowing charge to bleed off safely rather than accumulating for a destructive discharge.

Question 5

Explain, using free charges and Gauss's law, why the electric field inside a conductor must be zero in electrostatic equilibrium.

Model answer: A conductor contains free electrons that respond to any electric field. If any net field existed inside, it would exert a force on electrons, causing them to accelerate — which is a current, contradicting 'electrostatic' equilibrium. At equilibrium, all motion has ceased, so the net force on every electron is zero, meaning E = 0 everywhere inside. Applying Gauss's law to any closed surface drawn within the conductor: since E = 0, the flux is zero, so the enclosed charge is zero. Since this holds for any interior surface, no charge can reside in the interior — all excess charge must live on the outer surface.

The argument is self-consistent: free charges rearrange until E = 0, and then Gauss's law confirms that their redistribution to the surface is the only arrangement consistent with E = 0 inside.