Electric charge is uniformly distributed inside a nonconducting sphere of radius 0.30 m. The electric field at a point P, which is 0.50 m from the center of the sphere, is 15,000 N/C and is directed radially outward. At what distance from the center of the sphere does the electric field have the same magnitude as it has at P?
A) 0.11 m
B) 0.13 m
C) 0.15 m
D) 0.17 m
E) at no other point

Question

Quizplus · Accepted Answer

The electric field inside a uniformly charged sphere is given by:$$E = \frac{1}{4\pi\varepsilon_0} \frac{Q}{r^2}$$where Q is the total charge, r is the distance from the center of the sphere, and $\varepsilon_0$ is the permittivity of free space.At point P, r = 0.50 m and E = 15,000 N/C. So,$$15,000 N/C = \frac{1}{4\pi(8.85	imes10^{-12} C^2/Nm^2)} \frac{Q}{(0.50 m)^2}$$Solving for Q, we get:$$Q = 1.41	imes10^{-9} C$$Now, we want to find the distance r' at which the electric field is the same as at point P. So,$$15,000 N/C = \frac{1}{4\pi(8.85	imes10^{-12} C^2/Nm^2)} \frac{1.41	imes10^{-9} C}{(r')^2}$$Solving for r', we get:$$r' = 0.11 m$$Therefore, the correct answer is A.

Electric Charge Is Uniformly Distributed Inside a Nonconducting Sphere of Radius