Question

A sphere of radius R has an electric charge uniformly distributed in its entire volume at a distance D from the centre inside the sphere(D<R) the electric field intensity is directly proportional to
1)1/D. 2)1/D^2
3)D. 4)D^2​

Answer 1

Here ans is 3)D
As E=kQr/R^3( from inside the sphere)
So,E is directly proportional to r but here D<R therefore E is directly proportional to D.
Hope u got it

Answer 2

option (3) is correct.

A sphere of radius R has electric charge uniformly distributed in its entire volume.

Let charge Q is uniformly distributed in entire volume of sphere.

now at a distance d from the centre inside the sphere , charge will be q = Q/{4/3 πR³} × {4/3 π d³}

q = Qd³/R³ ..........(1)

from Gauss law,

electric flux through gaussian surface is the ratio of net charge enclosed inside the surface and permittivity of medium.

e.g., electric flux = q/$\epsilon_0$

[ we assumed, medium is air or vaccum]

now, electric flux = electric field × area of gaussian surface = q/$\epsilon_0$

electric field × 4πd² = Qd³/R³/$\epsilon_0$

or, electric field , E = Qd/4π$\epsilon_0$R³

here it is clear that E is directly proportional to d.