Question

If $V$ and $u$ are electric potential and energy density, respectively, at a distance $r$ from a positive point charge, then which of the following graphs is correct?

• A.
• B.
• C.
• D.

Answer 1

Answer: (C)

Electric potential due to a point charge at a point is, $V=\frac{k Q}{r}$
Electric potential due to a point charge at a point is, $E=\frac{k Q}{r^{2}}$
We know that, energy density due to electric field,
$u=\frac{1}{2}\epsilon _{0}E^{2}=\frac{1}{2}\frac{\epsilon _{0} k^{2} Q^{2}}{r^{4}}$
On replacing $r$ ,
$u=\left(\frac{1}{2} \frac{\epsilon _{0}}{k^{2} Q^{2}}\right)V^{4}$
$\therefore $ $V^{4} \propto u$