First slide

Dipole

Question

The magnitude of the electric field intensity at point $B (2, 0, 0)$ due to a dipole moment, $\vec{P} = \hat{i} + \sqrt{5} \hat{j}$ kept at origin is $n \times K$ (assume that the point B is at large distance from the dipole and $K = \frac{1}{4 π ε_{0}}$ ) (All quantities are in S.I units) Find n.

Moderate

Solution

The dipole is inclined at an angle
$\tan^{- 1} (\sqrt{5}) = θ \cos θ = \frac{1}{\sqrt{6}}$
To x-axis whereas the given point line on x-axis.
Also, $p = \sqrt{1^{2} + {(\sqrt{5})}^{2}} = \sqrt{6}$
r=2
$E = \frac{k p}{r^{3}} \sqrt{1 + 3 \cos^{2} θ} = k \frac{\sqrt{9}}{8} = 0.375 k$

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