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The diagram shows the cross-section of a long cylinder having radius $R$. The charge carried by the cylinder is NOT uniform; the charge density varies with radius according to the equation $\rho = A\,\sqrt{r}$.

Which of the following expressions gives the electric field strength at point $P$, a point that lies inside the cylinder and is a distance $r$ from the center of the cylinder?

A

$\dfrac{A\sqrt{r}}{\epsilon_0}$

B

$\dfrac{A\,\sqrt{r}}{3\,\pi \,\epsilon_0}$

C

$\dfrac{A\,\sqrt{r^3}}{2\,\epsilon_0}$

D

$\dfrac{4A\,\sqrt{r^5}}{7\,\epsilon_0}$

E

$\dfrac{2A\,\sqrt{r^3}}{5\,\epsilon_0}$

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