?

AP® Physics C: E & M

Free Version

Upgrade subject to access all content

Moderate

$Q_{enc}$ Cylinder 3

APPHEM-UKE2GS

The diagram shows a cylinder of radius $R$ that carries a charge that is uniformly distributed throughout its volume. The cylinder has a charge per unit length of $\lambda$.

A Gaussian surface is imagined that is also shown in the diagram. This Gaussian surface is also a cylinder having the same axis as the charged cylinder. The Gaussian cylinder's radius is $a$, where $a < R$, and its length is $L$.

What is the charge enclosed in the Gaussian cylinder?

A

$Q_{enc} = \lambda \dfrac{a}{R}$

B

$Q_{enc} = \lambda L\dfrac{a}{R}$

C

$Q_{enc} = \lambda L\dfrac{a^3}{R^3}$

D

$Q_{enc} = \lambda \dfrac{a^3}{R^3}$

E

$Q_{enc} = \lambda L\dfrac{a^2}{R^2}$