The electric field just outside the surface of a hollow conducting sphere of radius 20 cm has a magnitude of 500 N/C and is directed outward. An unknown charge Q is introduced into the center of the sphere and it is noted that the electric field is still directed outward but has decreased to 100 N/C. What is the magnitude of the charge Q?

Question

Quizplus · Accepted Answer

The electric field outside a conducting sphere is given by $E = \frac{kQ}{r^2}$, where $E$ is the electric field, $k$ is Coulomb's constant ($8.99 \times 10^9 \, \text{N m}^2/\text{C}^2$), $Q$ is the charge, and $r$ is the radius of the sphere. Given the electric field decreases from 500 N/C to 100 N/C when charge Q is introduced, and the radius is 0.2 m, we can solve for Q using the formula for the electric field. The decrease in electric field strength indicates that the charge introduced causes a redistribution of charges that results in a lower net electric field outside the sphere. By substituting the given values into the formula and solving for Q, we find that the magnitude of the charge Q that matches the given conditions is closest to 1.8 nC.

The Electric Field Just Outside the Surface of a Hollow