Question

A sphere of radius R has electric charge uniformly distributed in its entire volume. At a distance d from the center inside the sphere (d<R) the electric field intensity is directly proportional to ​

Answer 1

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.

Answer 2

Answer:

see here is your answer