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Two point dipoles $p \hat{k} & \frac{p}{2} \hat{k}$ are located at (0, 0, 0) & (1 m, 0, 2 m) respectively. The resultant electric field due to the two dipoles at the point (1 m, 0, 0) is

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$\frac{9 p}{32 {πϵ}_{0}} \hat{k}$

none of these

$\frac{7 p}{32 {πϵ}_{0}} \hat{k}$

$\frac{- 7 p}{32 {πϵ}_{0}} \hat{k}$

answer is B.

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Detailed Solution

$\vec{E_{(1)}} = \frac{P}{4 π \in_{0} (1)^{3}} - \hat{k}$

and $\vec{E_{(2)}} = \frac{P / 2 \times 2}{4 π \in_{0} (2)^{3}} \hat{k}$

Net electric field due to the two dipoles is $= \vec{E_{(1)}} + \vec{E_{(2)}} = \frac{- 7}{32} \frac{P}{{πϵ}_{0}} \hat{k}$

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