Question 239: Electrostats & Capacitance

Question

The electrostatic potential $\left(\phi_right)$ of a spherical symmetric system, kept at origin, is shown in the adjacent figure, and given as
$$ \begin{array}{ll} \phi_r=\frac{q}{4 \pi \epsilon_0 r} & \left(r \geq \mathrm{R}_0ight) \ \phi_r=\frac{q}{4 \pi \epsilon_0 \mathrm{R}_0} & \left(r \leq \mathrm{R}_0ight) \end{array} $$
Which of the following option(s) is/are correct?

Accepted Answer

(A) Since, potential is same, so electrostatic energy stored is zero.
(B)
$$ 	ext { (C) There is no charge in air, } 	herefore r=\mathrm{R}_0 $$
(D) From $r=\mathrm{R}_0$ to $\infty$.
We can assume point charge at centre equivalent to $q$.
$$ 	ext { So, } \overrightarrow{\mathrm{E}} \propto \frac{1}{r^2} 	ext { so, it is discontinuous } $$

Answer

For spherical region $r \leq \mathrm{R}_0$, the total electrostatic energy stored is zero.

Answer

Within $r=2 \mathrm{R}_0$, the total charge is $q$.

Answer

There will be no charge anywhere except at $r=\mathrm{R}_0$.

Answer

Electric field is discontinuous at $r=\mathrm{R}_0$.

Electrostats & Capacitance

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