Q. Two point dipoles $p \hat{k}$ and $\frac{p}{2} \hat{k}$ are located at $(0,0,0)$ and $(1\, m , 0,2\, m )$ respectively. The resultant electric field due to the two dipoles at the point $(1 \,m , 0,0)$ is
VITEEEVITEEE 2016
Solution:
The given point is on axis of $\frac{\hat{p}}{2}$ dipole and at equatorial line of $\hat{p}$ dipole so that field at given point is $\left(\hat{E}_{1}+\hat{E}_{2}\right)$
$\vec{E_{1}}=\frac{2 K(p 2)}{2^{3}}=\frac{K p}{8}(+\hat{k})$
$\vec{E_{2}}=\frac{K p}{1}(-\hat{k}) $
$\vec{E_{1}}+\vec{E_{2}}=-\frac{7}{8} K p(-\hat{k})=-\frac{7 p}{32 \pi \varepsilon_{0}} \hat{k}$
