Electrostatic potential is constant throughout the volume of a cond...

Question

Electrostatic potential is constant throughout the volume of a conductor and has the same value on its surface. Why?

Accepted Answer

📌 Explanation:

Step 1 — Inside the Conductor:
• In electrostatic equilibrium, the electric field inside a conductor is E = 0.
• Relation: E = −dV/dr
• Since E = 0 → dV/dr = 0 → V = constant inside.

Step 2 — On the Surface:
• The electric field at the surface is always perpendicular to the surface.
• There is no tangential component of E on the surface.
• No tangential E → no change in V along the surface → V = constant on surface.

Step 3 — Continuity:
• The potential just inside = potential on surface (by continuity of potential).

∴ Electrostatic potential is uniform throughout the volume and on the surface of a conductor.

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