For a non - conducting charged solid sphere of radius R. Which of the following graph shows the variation of electric field with increasing distance r from the center?

CONCEPT:

Gauss's law:

• According to Gauss law, the total electric flux linked with a closed surface called Gaussian surface is \(\frac{1}{ϵ_o}\) the charge enclosed by the closed surface.

\(⇒ ϕ=\frac{Q}{ϵ_o}\)

Where ϕ = electric flux linked with a closed surface, Q = total charge enclosed in the surface, and ϵo = permittivity​

EXPLANATION:

Case 1:

• The electric field intensity at a point inside a non - conducting charged solid sphere of radius R is given by

\(⇒ E = \frac{r\rho}{3\epsilon}\)     ...1)

Here, ϵ = electrical permittivity of the material of the insulating sphere, q' = charge enclosed by a sphere S, and r = radius of a sphere S

• From the above, it is clear that the electric field intensity at a point inside a non - conducting charged solid sphere varies directly proportional to the distance of the point from the centre of the sphere. 

Case 2:

• At the centre of the sphere, r = 0, the electric field intensity at a point inside a non - conducting charged solid sphere of radius R is zero.

Case 3:

• At the surface of the sphere, r = R

\(⇒ E = \frac{r\rho}{3\epsilon}= maximum\)

Case 4:

• At the surface outside the sphere, r > R

\(⇒ E = \frac{q}{4\pi ϵ _0 r^2}\)

• From the above, it is clear that the electric field intensity at a point outside a non - conducting charged solid sphere varies inversely proportional to the distance of the point from the centre of the sphere.
• The correct graph shows that shows the variation of the electric field with increasing distance r from the center

Hence option 2 is correct.