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

(A) $\frac{9 p}{32 \pi \epsilon_{0}}$

(B) $\frac{-7 p}{32 \pi e_{0}}$

(C) $\frac{7 p}{32 \pi \epsilon_{0}}$

(D) none of these

The given point is at axis of $\frac{\vec{p}}{2}$ dipole and at equatorial line of $P$ dipole so total field at given point is.

$\vec{E}=-\frac{k \vec{P}}{(1)^{3}}+\frac{2 k(\vec{P} / 2)}{(2)^{3}}$

$=k \vec{P}\left(-1+\frac{1}{8}\right)=\frac{-7 \vec{P}}{32 \pi \pi_{0}}$

So, The correct option of this question is (B).

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