Question

Derive electric potential energy due to an electric dipole

Answer 1

here is your answer hope it helps

Answer 2

Answer:-

$\overrightarrow{E} = \frac{1}{4\pi\epsilon_0} [\frac{q}{({r-a})^{2}} - \frac{q}{({r+a})^{2}}].\hat{p}$

$\overrightarrow{E} = \frac{q}{4\pi\epsilon_0}[\frac{({r+a})^{2} - ({r-a})^{2} }{(r^{2}- {a}^{2} )^{2}}].\hat{p}$

$\overrightarrow{E} = \frac{q}{4\pi\epsilon_0} = [\frac{4ra }{(r^{2}- {a}^{2} )^{2}}].\hat{p}$

$\overrightarrow{E} = \frac{1}{4\pi\epsilon_0} - \frac{2pr}{(r^{2}- {a}^{2} )^{2}}.\hat{p}$

→ Here, [p = q(2a)]

$\overrightarrow{E} = \frac{1}{4\pi\epsilon_0} - \frac{2p}{r^{3}}.\hat{p}$

$\overrightarrow{E} = \frac{1}{4\pi\epsilon_0} - \frac{2p}{r^{3}}$

→ [For r >> a]

Hence proved!