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AP® Physics C: E & M

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Moderate

$Q_{enc}$ Sphere 6

APPHEM-KHEVO7

The diagram shows a sphere of radius $R$ that carries a charge density that is not uniform. The charge density varies according to radial distance $R$ from the center of the sphere according to the equation $\rho = \dfrac{C}{r^2}$.

The diagram also shows the cross-section of a Gaussian sphere of radius $a$ that is concentric with the charged sphere.

Which of the following expresses the charge enclosed in the Gaussian sphere?

A

$\dfrac{2}{3}\,\pi \,C\,{a}^{2}$

B

$2\,\pi\,C$

C

$\pi \,C\,a$

D

$4\,\pi \,C\,A$

E

$\dfrac{4}{3}\,\pi \,C\,a$