Question

A Hollow charged metal sphere has radius r .If the potential difference between its surface and a point at a distance 3r from the centre is V ,then the electric field intensity at a distance 3r from the centre is?? thank u!!

Answer 1

`1/6 V/r`

Explanation:

The charge `Q` on a hollow metal sphere is uniformly distributed on its surface. This means that the potential and electric field outside the sphere are the same as these quantities for a point charge `Q` placed at the center of the sphere.

Thus, the potential difference between the surface and the point at a distance `3r` is

`V = 1/(4pi epsilon_0)(Q/r-Q/(3r)) = 2/3 1/(4pi epsilon_0)Q/r`

The electric field at this point is

`E = 1/(4pi epsilon_0) Q/(3r)^2 = 1/9 1/(4pi epsilon_0)Q/r^2 = 1/9 (3/2 V)/r = 1/6 V/r`