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 .

Difficult

Solution

The dipole is inclined at an angle
$\begin{array}{l} \tan^{- 1} (\frac{\sqrt{5}}{1}) = θ \\ \Rightarrow \cos θ = \frac{1}{\sqrt{1^{2} + {(\sqrt{5})}^{2}}} = \frac{1}{\sqrt{6}} \end{array}$
To $x - axis$ whereas the given point line on $x - axis$ .
Also, $p = \sqrt{{(1)}^{2} + {(\sqrt{5})}^{2}} = \sqrt{6}$
$E = \frac{k p}{r^{3}} \sqrt{1 + 3 \cos^{2} θ} = \frac{k \sqrt{6}}{2^{3}} \sqrt{1 + 3 {(\frac{1}{\sqrt{6}})}^{2}} = k \frac{\sqrt{9}}{8} = 0.375 k$ =0.38k

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