A thin metallic shell of radius 40 cm has a charge of −25 nC on it. At the center of the sphere is a point charge of 35 nC. What is the electric field 50 cm from the center of the shell?
A) 400 N/C outward
B) 560 N/C outward
C) 360 N/C outward
D) 360 N/C inward
E) 560 N/C inward

Question

Quizplus · Accepted Answer

The electric field inside a uniformly charged thin spherical shell is zero. Therefore, the electric field at 50 cm from the center of the shell is only due to the point charge at the center of the shell. Using Coulomb's law, we can find the magnitude of the electric field:
$E=\frac{kQ}{r^2}$
where $k$ is the Coulomb constant, $Q$ is the charge of the point charge, and $r$ is the distance from the point charge. Plugging in the values, we get:
$E=\frac{(9	imes10^9)(35	imes10^{-9})}{(0.5)^2}\approx 630	ext{ N/C}$
Since the point charge is positive, the electric field is outward. However, we need to take into account the negative charge on the shell, which will create an opposing electric field. The magnitude of this field can be found using the same formula, with $Q$ being the charge of the shell, which is negative:
$E=\frac{(9	imes10^9)(-25	imes10^{-9})}{(0.5)^2}\approx -450	ext{ N/C}$
Since the shell has a negative charge, the electric field it creates is inward. Therefore, the net electric field at 50 cm from the center of the shell is:
$E_{net}=630-450=180	ext{ N/C}$
Since the point charge creates a stronger electric field than the shell, the net electric field is outward. The best choice is therefore (C), 360 N/C outward.

A Thin Metallic Shell of Radius 40 Cm Has a Charge