The potential (in volts ) of a charge distribution is given by

$V(z)\, = \,30 - 5{z^2}for\,\left| z \right| \le 1\,m$

$V(z)\, = \,35 - 10\,\left| z \right|for\,\left| z \right| \ge 1\,m$

$V(z)$  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 $\left| z \right|\, \le 1\,\,m$  and $P_0 = 0$ elsewhere

• C

  ${\rho _0}\, = \,20\,{\varepsilon _0}$ for $\left| z \right|\, \le 1\,\,m$  and $P_0 = 0$ elsewhere

• D

  ${\rho _0}\, = \,40\,{\varepsilon _0}$ in the entire region