Question

A solid nonconducting sphere of radius R carries a charge Q distributed uniformly throughout its volume. At a certain distancer1 (r1< R) from the center of the sphere, the electric field has magnitude E. If the same charge Q were distributed uniformly throughout a sphere of radius 2R, the magnitude of the electric field at the same distancer1 from the center would be equal to ___________.

Answer 1

Answer:

The magnitude of the electric field in the second case will be $\frac{1}{8}$ of the electric field in the first case

Explanation:

The electric field at a distance $r_1$ < R from the center of the sphere is given by

the formula $E_1$  = $\frac{kQr_1}{R^3}$  

where R is the radius of the sphere, and, Q is the charge uniformly distributed on the sphere.

It is given that the same charge Q is distributed uniformly throughout a sphere of radius 2R and we have to find the electric field at same distance $r_1$ from the center.

In the second case the electric field will be given by

$E_2$ = $\frac{kQr_1}{(2R)^3} = \frac{kQr_1}{8R^3} =\frac{1}{8} \frac{kQr_1}{R^3} = \frac{1}{8} E_1$

Therefore the magnitude of the electric field in the second case will be $\frac{1}{8}$ of the electric field in the first case.