Moderate# $Q_{enc}$ Cylinder 7

APPHEM-B1L4JG

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 $\rho = C\,\sqrt{r}$. 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?