electric potential

Question

The electric potential at the centre of a charged hollow metal sphere is:

RankGuru · Accepted Answer

1. **Inside a Charged Conductor**: For a hollow metal sphere (or any conductor) in electrostatic equilibrium, the electric field ($E$) is zero everywhere inside.
2. **Relation between E and V**: $E = -\frac{dV}{dr}$. If $E = 0$, then $V$ must be constant.
3. **Boundary Condition**: The potential must be continuous across the surface.
4. **Conclusion**: Since the potential is constant inside and equal to the surface value, the potential at the center is the same as that on the surface.

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