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Two point dipoles of dipole moments 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 :  

Option: 1

\frac{9p}{32 \pi \epsilon_{0} } \hat{k}


Option: 2

\frac{-7p}{32 \pi \epsilon_{0} } \hat{k}


Option: 3

\frac{7p}{32 \pi \epsilon_{0} } \hat{k}


Option: 4

none of these


Answers (1)

best_answer

we have studied that Electric field at a point on the axis of dipole is given by:-

\vec{E}_{net}=\frac{2 K \vec{P}}{r^{3}}=\frac{2 \vec{P}}{4 \pi \epsilon_{0} r^{3}}

and Electric field at a point on the equitorial line is given by:-

\vec{E}_{net}=\frac{ -K \vec{P}}{r^{3}}=\frac{ -\vec{P}}{4 \pi \epsilon_{0} r^{3}}

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

 

\vec{E}=\frac{k\vec{P}}{(1)^{3}}+\frac{2k\left (\vec{P} /2 \right )}{(2)^{3}}=k\vec{P}\left ( -1+\frac{1}{8} \right )=\frac{-7\vec{P}}{32 \pi \epsilon _{0}}

Posted by

Suraj Bhandari

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