Question

There are two concentric spherical shells of radii r and 2r . Initially a charge Q is given to the inner shell . Now , switch S1 is closed and opened then S2 is closed and opened and the process is repeated n times for both the keys alternatively . Find the final potential difference between the shells

Answer 1

Difference in potential =  - kq/2r

Explanation:

Given: There are two concentric spherical shells of radii r and 2r . Initially a charge Q is given to the inner shell . Now , switch S1 is closed and opened then S2 is closed and opened and the process is repeated n times for both the keys alternatively.

Find: The final potential difference between the shells.

Solution:

When the thickness of the shell is negligible, the potential energy at the center is kq/R where k is the constant (9 *10^9 N), q is the amount of charge present and R is the radius of the the shell.

Potential of the inner shell = kq/r

Potential of the outer shell = kq/2r

Difference in potential = kq/2r - kq/r = kq/r (-1/2) = - kq/2r