A solid nonconducting sphere of radius R carries a charge Q distributed uniformly throughout its volume.At a certain distance r₁ (r₁

Question

A solid nonconducting sphere of radius R carries a charge Q distributed uniformly throughout its volume.At a certain distance r₁ (r₁ < R)from the center of the sphere,the electric field has magnitude E.If the same charge Q were distributed uniformly throughout a sphere of radius 2R,the magnitude of the electric field at the same distance r₁ from the center would be equal to A) E/8. B) E/2. C) 2E. D) 8E. E) E.

Quizplus · Accepted Answer

From Gauss's Law, we know that the electric field at a distance r from the center of a uniformly charged sphere of radius R and total charge Q is given by:

E = K * Q * r / R^3

where K = 1 / (4πε0) is the Coulomb constant and ε0 is the permittivity of free space.

If we take the ratio of the electric field at distance r from the center of a sphere of radius R with charge Q to the electric field at distance r from the center of a sphere of radius 2R with charge Q, we get:

E(R) / E(2R) = (K * Q * r / R^3) / (K * Q * r / (2R)^3)
              = 1 / 8

Therefore, the magnitude of the electric field at distance r from the center in the second case is:

E'(r) = E(r) / 8
      = E / 8

So the answer is A) E/8.

A Solid Nonconducting Sphere of Radius R Carries a Charge