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Properties of Field Lines

Two point dip...

Question

Two point dipoles $(\frac{p}{2})$ and $p$ are located at $(0, 0, 0)$ and $(1 m, 0, 2 m)$ respectively both are parallel to x-axis resultant electric field due to the dipoles at the point $(1 m, 0, 0)$ is:-

A

\frac{9 p}{32 π ϵ_{0}}^i

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B

\frac{- 7 p}{32 π ϵ_{0}}^i

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C

\frac{- 7 k p^i}{8}

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D

None of these

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Solution

The correct option is C $\frac{- 7 k p^i}{8}$
$\begin{matrix} d u e t o (\frac{p}{2}) \to E = \frac{2 k p}{2 r^{2}}^i = k p^i d u e t o (p) \to E = - \frac{K P}{r^{3}}^i = - \frac{K P}{8}^i E_{n e t} = \frac{- 7 k p^i}{8} H e n c e, t h e o p t i o n C i s c o r r e c t . \end{matrix}$

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