A solid sphere of radius has a charge distributed in its volume with a charge density

PHYSICS · Subjective · AP · Physics C: Electricity and Magnetism · Electric Charges Fields and Gauss's Law · Electric Charges Fields and Gauss's Law

Problem

A solid sphere of radius

R

has a charge

Q

distributed in its volume with a charge density

\rho = kr^a

, where

k

and

a

are constants and

r

is the distance from its centre. If the electric field at

r = \frac{R}{2}

\frac{1}{8}

times that at

r = R

, find the value of

a