Question 627: Electrostats & Capacitance

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.

Accepted Answer

We know,
E(z) = $$-$$ $${{dv} \over {dz}}$$
$$ 	herefore $$   E(z) = $$-$$ 10 z for $$\left| z ight| \le 1$$ m
and E(z) = 10 for $$\left| z ight| \ge 1$$ m
$$ 	herefore $$   The source is an infinity large non conducting  thick of thickness z = 2 m.
$$ 	herefore $$   E = $${\sigma  \over {2{\varepsilon _0}}}$$ = $${{ho \left( 2 ight)} \over {2{\varepsilon _0}}}$$ = $${ho  \over {{\varepsilon _0}}}$$
$$ 	herefore $$   $${ho  \over {{\varepsilon _0}}}$$ = 10
$$ \Rightarrow $$   $$ho $$ = $${10\,{\varepsilon _0}}$$

Answer

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

Answer

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

Answer

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

Answer

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

Electrostats & Capacitance

Choose the correct answer: