A spherical,non-conducting shell of inner radius = 10 cm and outer radius = 15 cm carries a total charge Q = 15 μC distributed uniformly throughout the volume of the shell.What is the magnitude of the electric field at a distance r = 12 cm from the center of the shell?
A) 5.75 × N/C
B) zero
C) 2.87 × N/C
D) 5.75 × N/C
E) 2.87 × N/C

Question

A spherical,non-conducting shell of inner radius  = 10 cm and outer radius  = 15 cm carries a total charge Q = 15 μC distributed uniformly throughout the volume of the shell.What is the magnitude of the electric field at a distance r = 12 cm from the center of the shell? 
A) 5.75 × N/C 
B) zero 
C) 2.87 × N/C 
D) 5.75 × N/C 
E) 2.87 × N/C

Quizplus · Accepted Answer

Since the charge is uniformly distributed on the shell, at any point inside the shell, the electric field is zero. At a distance r=12 cm, the point is inside the shell, so the electric field at that point is zero. Therefore, the correct answer is B). However, if the point is outside the shell, the electric field can be found using Coulomb's law, which is E=kQ/r^2, where k is Coulomb's constant, Q is the total charge on the shell, and r is the distance from the center of the shell. In this case, r=12 cm, so the electric field is E=kQ/r^2=9x10^9 Nm^2/C^2 x 15x10^-6 C/(0.12 m)^2 = 2.87x10^4 N/C = C).

A Spherical,non-Conducting Shell of Inner Radius = 10 Cm