A hollow metal sphere of radius R is given +Q charges to its outer surface. The electric potential at a distan

Question

A hollow metal sphere of radius R is given +Q charges to its outer surface. The electric potential at a distance R/3 from the centre of the sphere will be:

Accepted Answer

1. **Properties of a Conductor:** For a charged hollow metal sphere (a conductor), the charge resides entirely on the outer surface. The electric field inside the conductor is zero.
2. **Potential Inside:** Since the electric field ($E = -dV/dr$) is zero inside ($r < R$), the electric potential ($V$) is constant throughout the interior volume and is equal to the potential at the surface.
3. **Calculation:** The point in question is at a distance $r = R/3$ from the center. Since $R/3 < R$, the point lies inside the sphere.
   Therefore, $V_{inside} = V_{surface} = \frac{1}{4\pi\varepsilon_0}\frac{Q}{R}$.
   (This behavior is analogous to the gravitational potential inside a spherical shell discussed in Class 11 Physics, Chapter 8).

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