Question

A solid nonconducting sphere of radius R carries a charge Q distributed uniformly throughout its volume. At a certain distance rl (r (A) E/8

(B) E 78.
(C) E/2
(D) 2E
(E) 8E

Answer 1

A ) E/8

Step-by-step explanation:

If the sphere of radius R carries charge Q, then the volumetric charge density is:

ρ₁ = [Q/ (4/3)*π*R³]

Therefore the net charge inside r ( r < R ) is:

q₁ = ρ * (4/3)*π*r³

And E = K * q₁/r K = 9,98 *10⁹ [N*m²/C²]

E = K * ρ * (4/3)*π*r³/r

E = K * ρ * (4/3)*π*r²

If now the charge is distributed over a sphere of radius 2R

ρ₂ = [Q/ (4/3)*π*(2R)³]

ρ₂ = [Q/ (4/3)*π*8*R³]

Then ρ₂ < ρ₁ in fact ρ₂ = (1/8)*ρ₁

The electric field depends on the net charge enclosed by a gaussian surface, and the distance between the net charge and the considered point, ( considering the net charge as being at the center of the gaussian surface) In this case, there was no distance change then

E₂ = E₁/8

The right answer is lyrics A ) E/8