First slide

Potential energy

Question

At distance 'r' from a point charge, the ratio $\frac{U}{V^{2}}$ (where 'U' is energy density and 'V' is potential) is best represented by

Moderate

A
B
C
D

Solution

$U = \frac{1}{2} ε_{0} E^{2} = \frac{1}{2} \frac{ε_{0} K^{2} Q^{2}}{r^{4}} V = \frac{KQ}{r} \frac{U}{V^{2}} = \frac{\frac{1}{2} ε_{0} K^{2} \frac{Q^{2}}{r^{4}}}{\frac{K^{2} Q^{2}}{r^{2}}} = \frac{1}{2} \frac{ε_{0}}{r^{2}} Because \frac{U}{V^{2}} \propto \frac{1}{r^{2}}$
so the correct option is (b).

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