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AP® Physics C: E & M

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$Q_{enc}$ Sphere 1

APPHEM-SKSXVZ

The diagram shows a sphere of radius $R$ that carries a charge uniformly distributed throughout its volume. The volume charge density is $\rho$. A Gaussian sphere of radius $a$ is imagined that is concentric to the charged sphere.

If $a > R$, what is the charge enclosed in the Gaussian surface?

A

$Q_{enc} = 4\pi\rho R^2$

B

$Q_{enc} = \frac{4}{3}\pi\rho a^3$

C

$Q_{enc} = 4\pi\rho a^2$

D

$Q_{enc} = \frac{4}{3}\pi\rho R^3$

E

$Q_{enc} = \pi\rho a^2$