Question

Radius of a non-conducting sphere is 'R', volume charge density is 'p'. Electric field at a
distance of 'r' (r<R) is
(a) E proportional to r^2
(b) E proportional to r^-1
(c) E proportional to r
(d) E proportional to r^-2​

Answer 1

Explanation:

Correct option is

B

2

Given that volume charge density ρ=Cr

2

Total charge on the sphere q=∫

0

r

4πr

2

drρ=∫

0

r

4πCr

4

dr

=

5

4

πCr

5

E

r=R/2

(R/2)

2

kq

(r=R/2)

=

(R/2)

2

k(4/5)πC(R/2)

5

E

r=2R

=

(2R)

2

kq

(r=R)

=

4R

2

k(4/5)πCR

5

Now solve to get

E

r=R/2

E

r=2R

=2