A conducting sphere of radius $a$ initially contains a uniform volume charge density $\rho$. What is the electric flux $\Phi$ through a spherical surface of radius $2 a$ centered at a point on the surface of the charged sphere (see figure) at a later time $t$ ? ( $\epsilon_0$ is the permittivity of free space.)

• A

  $\Phi=\frac{4}{\epsilon_0} \pi a^2 \rho$
• B

  $\Phi=\frac{32}{3 \epsilon_0} \pi a^3 \rho$
• Correct answer
  C

  $\Phi=\frac{4}{3 \epsilon_0} \pi a^3 \rho$
• D

  $\Phi=\frac{16}{\epsilon_0} \pi a^2 \rho$

Hence, the correct answer is option: 'C'.