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?

2E

Explanation:

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

(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:

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

Substituting into (1), we find:

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

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c. magnitude and direction