Difficult# $E$ Outside Cylinder 2

APPHEM-HKYVGY

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 $\rho = A\,r^2$.

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