Question

Two point dipoles $p\hat{k}$ and $\frac{p}{2}\hat{k}$ are located at (0,0,0) and (1m,0,2m). Find the field at the point (1,0,0).

• A. $\frac{9p}{32\pi {\epsilon }_0}\hat{k}$
• B. $\frac{-7p}{32\pi {\epsilon }_0}\hat{k}$
• C. $\frac{7p}{32\pi {\epsilon }_0}\hat{k}$
• D. none of these

Answer 1

The correct option is B $\frac{-7p}{32\pi {\epsilon }_0}\hat{k}$

The given point is on axis of $\frac{\overline{p}}{2}$ dipole and at equatorial line of $\overline{p}$ dipole so that field at given point is $(\overline{E_1}+\overline{E_2})$
$\overline{E_1}=\frac{2K\left(p/2\right)}{2^3}=\frac{Kp}{8}(+\hat{k})$
$\overline{E_2}=\frac{Kp}{1}(-\hat{k})$
$\overline{E_1}+\overline{E_2}=\frac{7}{8}Kp(-\hat{k})=-\frac{7p}{32\pi {\epsilon }_0}\hat{k}$