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Gravitation vs. Electrostatics

If the potent...

Question

If the potential energy between electron and proton at a distance r is given by $U = - (\frac{k e^{2}}{3 r^{3}})$ . The force is :

A

F = \frac{k e^{2}}{r^{2}}

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B

F = - \frac{3}{4} \frac{k e^{2}}{r^{4}}

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C

F = \frac{k e^{2}}{r^{4}}

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D

F = \frac{k e^{2}}{r}

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Solution

The correct option is C $F = \frac{k e^{2}}{r^{4}}$
$F = - \frac{d u}{d r}$
$= - \frac{d}{d r} (- \frac{K e^{2}}{3 r^{3}}) = - \frac{K e^{2}}{r^{4}}$

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