A small electric dipole p→$$=10$$−$$9$$ $$i^$$ $$N/C$$ is placed at the origin. $$A(1$$,$$0m)$$ and $$B(0$$,$$1m)$$ are two points. Then (VA$$−$$VB) is

Potential Energy of dipole in external field

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A small electric dipole $\vec{p} = 10^{- 9} \hat{i} N / C$ is placed at the origin. $A (1, 0 m)$ and $B (0, 1 m)$ are two points. Then $(V_{A} - V_{B})$ is

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Solution

x-axis is the equatorial line of the dipole and potential of any point on the equatorial line is zero.
Hence $V_{B} = 0$ and $V_{A} = \frac{1}{4 π \in_{0}} . \frac{p}{r^{2}} = 9 \times 10^{9} \times \frac{10^{- 9}}{{(1)}^{2}} V = 9 volt$
$∴ V_{A} - V_{B} = 9 volt .$

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