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

Question

Spheres of charge: 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

The electric field inside a uniformly charged sphere is proportional to the charge density and the distance from the center. If the sphere's radius is doubled, the charge density decreases by a factor of 8 (since volume increases by 2^3 = 8), thus reducing the electric field by the same factor.

Spheres of Charge: a Solid Nonconducting Sphere of Radius R