Question

A spherically-symmetric charge distribution takes the form
ρ(r)={A(1- R/r)}
{0
for r ≤ R,
for r> R,
where A is a positive constant.
(a)
What is the total charge Q in this charge distribution?
(b)
Find the electric field at a general point with r ≤ R. At what distance from the centre
of the charge distribution does the magnitude of the electric field have a maximum value?
Calculate the maximum value of the magnitude of the electric field, assuming that
Q =3.5 × 10−11Cand R =6.5cm.

Answer 1

(c)
Use Gauss’s law to find an expression for the divergence of the electric field at the radial
distance at which the electric field has its maximum magnitude.

Answer 2

E 4 pi R^2 = total enclosed charge / espsilon0

Answer 3

\[Q=\int\limits_{0}^{R}\int\limits_{0}^{2 \pi }\int\limits_{0}^{\pi}\rho(r) r^2\sin \theta dr d \theta d \phi \]

Answer 4

use Gauss's law to find the electric field...
then differentiate it wrt r to find the maximum magnitude of the electric field

Answer 5

do u know triple integral , spherical coordinate system?