Question

A charge of \( 6 \, \mu C \) is given to a hollow metallic sphere of radius 0.2 m. Find the potential at (i) the surface and (ii) the centre of the sphere.

Hint:

Remember that the potential inside a charged conductor is uniform and equal to the potential at its surface, regardless of the shape of the conductor.

Answer 1

Given: Charge \( Q = 6 \, \muC = 6  10^{-6} \, C \) Radius of the sphere \( R = 0.2 \, m \) 

 (i) Potential at the Surface of the Sphere The electric potential \( V \) at the surface of a charged sphere is given by: \[ V = \frac{kQ}{R} \] where \( k = \frac{1}{4\pi\epsilon_0} \approx 9 \times 10^9 \, N m}^2/C}^2 \). Substituting the given values: \[ V = \frac{9 \times 10^9 \times 6 \times 10^{-6}}{0.2} = \frac{54 \times 10^3}{0.2} = 270 \times 10^3 \, V} \] \[ V = \boxed{2.7 \times 10^5 \, V}} \] (ii) Potential at the Center of the Sphere For a hollow metallic sphere, the potential inside the sphere (including at the center) is the same as the potential at the surface. Therefore: \[ V_{center}} = V_{surface}} = \boxed{2.7 \times 10^5 \, V}} \]