Question

Find out the magnitude of electric field intensity and electric potential due to a dipole of moment $\overrightarrow{P}=\hat{i}+\sqrt{3}\hat{j}$ kept at origin at following points.
(i) $(2,0,0)$
(ii) $(-1,\sqrt{3},0)$

Answer 1

we have,

$E=E_1+E_2$

for axial dipole, $E_1=\frac{2kp}{r^3}$

for equatorial diploe, $E_2=\frac{kp}{r^3}$

$r(2,0,0)=2i$

$E_1=\frac{2k\times 1}{2^3}=\frac{k}{4}i$

$E_2=\frac{k\sqrt{3}}{2^3}=\frac{\sqrt{3}}{8}j$

$E=\sqrt{\frac{k^2}{16}+\frac{3k^2}{64}}=\frac{\sqrt{7}}{8}k$