$A$ spherical conducting shell of inner radius $r_1$ and outer radius $r_2$ has a net charge $Q$. $A$ point charge $-q$ is placed at the center of the shell. Determine the surface charge density on the inner and outer surfaces of the shell.

• A
  $\frac{q}{4 \pi r_1^2}$ and $\frac{Q-q}{4 \pi r_2^2}$
• B
  $\frac{q}{4 \pi r_1^2}$ and $\frac{Q}{4 \pi r_2^2}$
• C
  $\frac{-q}{4 \pi r_1^2}$ and $\frac{Q+q}{4 \pi r_2^2}$
• D
  zero and $\frac{Q-q}{4 \pi r_2^2}$