Question

Charge Q is distributed non-uniformly in a spherical volume with charge density p  varying with r but not depending on θ, ∅  in spherical coordinates. Let
                   

For a point at a distance  r  from the centre, the electric field must have a magnitude

(a) E for all values of  r

(b) E for r < R  but not for  r > R

(c) E for r > R but not for  r < R

(d) not equal to E  for any point

​

Answer 1

Answer:

If ρ be volume charge density, Q=ρ.

3

4

πR

3

...(1)

Consider a Gaussian surface of radius r. Using Gauss's law the field at r is

E.4πr

2

=

ϵ

0

ρ.

3

4

πr

3

E=

4πϵ

0

R

3

Qr

using (1)

∴E∝r

How satisfied are