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AP® Physics C: E & M

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Moderate

$Q_{enc}$ Cylinder 6

APPHEM-XGHYNY

The diagram shows a very long cylinder of radius $R$ that carries a charge density that is not uniform. The charge density varies according to radial distance $R$ from the axis of the cylinder according to the equation $\rho = \dfrac{C}{r}$. The diagram also shows the cross-section of a Gaussian cylinder of radius $a$ and length $L$ that is coaxial with the charged cylinder.

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

A

$2\,\pi \,C\,L\,a$

B

$2\,\pi \,C\,L$

C

$\dfrac{1}{2}\pi \,C\,L\,{a}^{2}$

D

$\pi \,C\,L\,a$

E

$4\,\pi \,C\,L\,a$