Question

Two short 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 $\frac{-n p}{32 \pi \varepsilon_{0}} \hat{k}$. Find $n$.

Answer 1

The given point is at axis of $\frac{\vec{p}}{2}$ dipole and at equatorial line of $\vec{p}$ dipole.
So, the total field at the given point is
$\vec{E}=-\frac{k \vec{p}}{(1)^{3}}+\frac{2 k(\vec{p} / 2)}{(2)^{3}}$
$=k \vec{p}\left(-1+\frac{1}{8}\right)=\frac{-7 \vec{p}}{32 \pi \varepsilon_{0}}$