Question

Charge Q is uniformly distributed throughout a spherical insulator of radius R. The electric field at a point a distance R/4 from the center of the shell is closest to:

A) ????????/???? 2 .
B) ????????/4???? 2
C) ????????/16???? 2
D) 16????????/???? 2
E) zero.

Answer 1

Step-by-step explanation:

We shall apply Gauss's law to calculate electric field at a point inside R .Let the point be at a distance r from the centre . Draw a sphere of radius r as gausssian surface . If ρ be the charge volume density

ρ = Q / 4πR³ /3

= 3Q / 4πR³

Charge inside Gaussian surface

q = 4πr³ /3 x ρ

Flux over the Gaussian surface

4πr² E where E is electric field at distance r

4πr² E = q / ε

= 4πr³ρ /3 ε

E = 4πr³ρ /(4πr² x 3ε)

= ρ r/ 3ε

= Qr / 4πR³

Put r = R /4

E = QR / 16πR³

= Q / 16πR²