Question

A solid nonconducting sphere of radius R carries a uniform charge density throughout its volume. At a radial distance R/4 from the center, the electric field has a magnitude E. What is the magnitude of the electric field at a radial distance R/2?

Answer 1

Answer:

2E

Explanation:

The electric field inside a charged, nonconducting sphere is given by

$E(r)=\frac{kQr}{R^3}$ (1)

where

k is the Coulomb's constant

Q is the total charge on the sphere

r is the distance from the centre of the sphere

R is the radius of the sphere

In this problem, the magnitude of the electric field at r = R/4 is E, so we can write:

$E=\frac{kQ(\frac{R}{4})}{R^3}=\frac{1}{4}\frac{kQ}{R^2}$

Then, we want to calculate the magnitude of the electric field at a distance of

$r=\frac{R}{2}$

Substituting into (1), we find:

$E'=\frac{kQ(\frac{R}{2})}{R^3}=\frac{1}{2}\frac{kQ}{R^2}=2E$

Therefore, the electric field at R/2 is twice the electric field at R/4.