#### Question

A spherical volume contains a uniformly distributed charge of density 2.0 × 10 ^{-4 }Cm^{-3} Find the electric field at a point inside the volume at a distance 4⋅0 cm from the centre.

#### Solution

Given :

Volume charge density, ρ = 2 ×10^{-4} C /m3

Let us assume a concentric spherical surface inside the given sphere with radius = 4 cm = 4 ×10^{-2} m

The charge enclosed in the spherical surface assumed can be found by multiplying the volume charge density with the volume of the sphere. Thus,

`"q" = ρ xx 4/3 pi"r"^3`

`=> "q"= (2 xx 10^-4) xx 4/3 pi"r"^3`

The net flux through the spherical surface,

`phi ="q"/∈_0`

The surface area of the spherical surface of radius r cm:

A = 4πr^{2}

Electric field,

`"E" = "q"/(∈_0 xx "A")`

`"E" = (2 xx 10^-4 xx 4 pi "r"^3)/(∈_0 xx 3 xx 4 pi"r"^2)`

`"E" = (2 xx 10 ^-4 xx "r")/(3 xx ∈ _0)`

The electric field at the point inside the volume at a distance 4⋅0 cm from the centre,

`"E" = ((2 xx 10^-4) xx (4 xx 10^-2))/(3 xx (8.55 xx 10^-12)) "N" // "C"`

`"E" = 3.0 xx 10^5 "N" // "C"`