Question

Consider an initially neutral hollow conducting spherical shell with inner radius r and outer radius 2r. A point charge +Q is now placed inside the shell at a distance r/2 from the centre. The shell is then grounded by connecting the outer surface to the earth. P is an external point at a distance 2r from the point charge +Q on the line passing through the centre and the point charge +Q as shown in the figure.
The magnitude of the force on a test charge +q placed at P will be

• A. $\frac{1}{4\pi {\epsilon }_0}\frac{qQ}{4r^2}$
• B. $\frac{1}{4\pi {\epsilon }_0}\frac{9qQ}{100r^2}$
• C. $\frac{1}{4\pi {\epsilon }_0}\frac{4qQ}{25r^2}$
• D. 0

Answer 1

Answer: (D)

0

Since the shell is a conducting one, we have electric field $\text{zero}$ inside the shell.

By the principle of charge induction, a charge of $-Q$ gets developed on the inner surface of the shell, such that the electric field is zero outside the inner surface.

Similarly, the unbalanced $+Q$ charge gets transferred to the outer surface. As the outer surface is grounded, the unbalanced charge $+Q$ gets transferred to Earth.

Thus, the entire charge system acts as a no charge, for all the points outside the inner shell.

Thus, the force acting on the test charge is $\text{zero}$ as the test point lies outside the inner surface of the shell.