A charge Q accumulates on the hollow metallic dome,of radius R,of a Van de Graaff generator.A probe measures the electric field strength at various points outside the sphere surface.If the probe is initially at a distance 3R from the sphere's center and then is moved to 5R,by what factor will the electric field reading change?

Question

Quizplus · Accepted Answer

The electric field strength at a distance r from the center of the hollow sphere can be found using the formula E = kQ/r^2, where k is Coulomb's constant. When the probe is initially at a distance 3R from the center, the electric field strength is given by E1 = kQ/(3R)^2 = kQ/9R^2. When the probe is moved to a distance of 5R from the center, the electric field strength is given by E2 = kQ/(5R)^2 = kQ/25R^2. The factor by which the electric field reading changes is E2/E1: E2/E1 = (kQ/25R^2)/(kQ/9R^2) E2/E1 = (9/25) E2/E1 = 0.36 Therefore, the electric field reading will decrease by a factor of 0.36, or 3/5, as the probe is moved from a distance of 3R to 5R. The correct answer is D, (3/5)².

A Charge Q Accumulates on the Hollow Metallic Dome,of Radius