The potential (in volts) of a charge distribution is given by. V(z) = 30 $-$ 5x2 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.

Question

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

V(z) = 30 $-$ 5x² 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.

${\rho _0}$ = 10 ${\varepsilon _0}$ for $\left| z \right|$ $ \le $ 1 m and ${\rho _0} = 0$ elsewhere

${\rho _0}$ = 20 ${\varepsilon _0}$ in the entire region

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

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

Solution

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