The potential (in volts) of a charge distribution is given by $V(z) = 30 - 5z^2$ for $|z| \le 1 \ m$ and $V(z) = 35 - 10|z|$ for $|z| \ge 1 \ m$. $V(z)$ does not depend on $x$ and $y$. If this potential is generated by a constant charge per unit volume $\rho_0$ (in units of $\varepsilon_0$) which is spread over a certain region,then choose the correct statement.

• A
  $\rho_0 = 20 \varepsilon_0$ in the entire region
• B
  $\rho_0 = 10 \varepsilon_0$ for $|z| \le 1 \ m$ and $\rho_0 = 0$ elsewhere
• C
  $\rho_0 = 20 \varepsilon_0$ for $|z| \le 1 \ m$ and $\rho_0 = 0$ elsewhere
• D
  $\rho_0 = 40 \varepsilon_0$ in the entire region