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Potential Energy of Two Point Charges

The electrost...

Question

The electrostatic potential $(ϕ_{r})$ of a spherical symmetric system, kept at origin, is shown in the adjacent figure, and given as
$ϕ_{r} = \frac{q}{4 π \in_{o} r} (r \geq R_{0})$
$ϕ_{r} = \frac{q}{4 π \in_{o} R} (r \leq R_{0}) R_{0} r$
Which ofthe following option(s) $i s / a r e$ correct?

A

For spherical region

r \leq R_{0}

, total electrostatic energy stored is zero.

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B

Within

r = 2 R_{0}

, total charge is

q

.

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C

There will be no charge anywhere except at

r = R_{0}

.

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D

Electric field is discontinuous at

r = R_{0}

.

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Solution

The correct options are
A For spherical region $r \leq R_{0}$ , total electrostatic energy stored is zero.
B Within $r = 2 R_{0}$ , total charge is $q$ .
C There will be no charge anywhere except at $r = R_{0}$ .
D Electric field is discontinuous at $r = R_{0}$ .

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