# The electric field in a region is radially outward with magnitude $E=A\;r\;$ . Find the charge contained in a sphere of radius a centered at the origin . Take $\;A=90\;Vm^{-2}\;$ and $\;a = 2m\;$

$(a)\;8 \mu C\qquad(b)\;0.8 \mu C\qquad(c)\;0.08 \mu C\qquad(d)\;80 \mu C$

Answer : (c) $\;0.08 \;\mu C$
Explanation : The electric field at the surface of the sphere is Aa and being radia it is along the outward normal . Therefore
$\phi=\oint\;E\;ds\;cos\;\theta=Aa\;(4\;\pi\;a^2)$
$Q=\in_{0}\phi=4\;\pi\;\in_{0}\;Aa^3$
$=(\large\frac{1}{9\times10^{9}})\;90\times8$
$Q=8\times10^{-8}\;C$