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Potential Energy - External Viewpoint

At distance '...

Question

At distance ‘r’ from a point charge, the ratio $\frac{u}{v^{2}}$ (where ‘u’ is energy density and ‘v’ is electric potential) is best represented by:

A

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B

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C

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D

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Solution

The correct option is B

$u = \frac{1}{2} ϵ_{0} E^{2} = \frac{1}{2} ϵ_{0} \frac{K^{2} Q^{2}}{r^{4}} v = \frac{K Q}{r} \frac{u}{v^{2}} \propto \frac{1}{r^{2}}$

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