Which of the following plots represents the variation of the electric field with distance from the centre of a uniformly charged non- conducting sphere of radius R?

Question

Which of the following plots represents the variation of the electric field with distance from the centre of a uniformly charged non- conducting sphere of radius R? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

The electric field intensity at a point lying outside the sphere (non-conducting) is

E = \frac{1}{4 π ε _{0}} \frac{q}{r ^{2}}

where

r

is the distance of that point from centre of sphere.

∴ E \propto \frac{1}{r ^{2}} \dots

(i)
The electric field intensity at surface of sphere

E = \frac{q}{4 π ε _{0} R ^{2}}

or

E \propto \frac{1}{R ^{2}} \dots

(ii)

R

, being the radius of sphere. The electric field intensity at a point lying inside the sphere is

E = \frac{q r}{4 π ε _{0} R ^{3}}

or

E \propto r \dots

(iii)
Also at the centre of sphere

r = 0.

Hence,

E = 0

.
The graphical distribution is shown below:

Q. Which of the following plots represents the variation of the electric field with distance from the centre of a uniformly charged non- conducting sphere of radius R?