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  4. 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?

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Q. 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?

NTA AbhyasNTA Abhyas 2020Electrostatic Potential and Capacitance

Solution:

$\text{V}=\frac{\textit{kQ}}{\textit{r}}$
we know that,
$u=\frac{1}{2}\epsilon _{0}\textit{E}^{2}=\frac{1}{2}\frac{\epsilon _{0} k^{2} Q^{2}}{r^{4}}$
$\therefore $ $\text{V}^{4} \propto u$