A 5.0-nC point charge is embedded at the centre of a non-conducting sphere (radius = 2.0 cm) which has a charge of -8.0 nC distributed uniformly throughout its volume.What is the magnitude of the electric field at a point that is 1.0 cm from the centre of the sphere?
A)1.8*105 N/C
B)9.0 * 104 N/C
C)3.6 * 105 N/C
D)2.7 *105 N/C
E)7.2 *105 N/C

Question

Quizplus · Accepted Answer

We can use the formula for electric field from a charged sphere:
$$E=\frac{1}{4\pi \epsilon_0}\frac{Q}{r^2}$$
where $Q$ is the charge within a sphere of radius $r$, centered at the same point as the point where we want to find the field, and $r$ is the distance from the center of the sphere to the point of interest.

In this case, we have a point charge of $5.0$ nC at the center of a sphere with radius $2.0$ cm, and charge $Q = 108$ nC distributed uniformly throughout its volume.

To find the electric field at a point $1.0$ cm from the center of the sphere, we use $r = 3.0$ cm in the above formula:
$$E=\frac{1}{4\pi \epsilon_0}\frac{Q}{r^2}=\frac{1}{4\pi \epsilon_0}\frac{(108 	imes 10^{-9} \; C)}{(0.03 \; m)^2} \approx 3.6 	imes 10^5 \; N/C$$

Therefore, the correct answer is (C).

A 50-NC Point Charge Is Embedded at the Centre of a a Non-Conducting