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Q.

The ratio of magnitudes of Electric field strength at $A (2, 0, 0)$ and at $B (2, 2 \sqrt{3}, 0)$ due to a short dipole having dipole moment $\vec{p} = \hat{i} + \sqrt{3} \hat{j}$ , kept at origin is:

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a

$8 \sqrt{7}$

b

$\frac{\sqrt{7}}{8}$

c

$2 \sqrt{7}$

d

1

answer is C.

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Detailed Solution

$E_{ax} = \frac{2 kp}{r^{3}} E_{eq} = \frac{kp}{r^{3}} here for point (2, 0, 0) \Rightarrow r = 2 E_{A} = E_{1} + E_{2} = \frac{2 k (1)}{2^{3}} \hat{i} + \frac{k (\sqrt{3})}{2^{3}} \hat{j} E_{A} = \sqrt{{(\frac{k}{4})}^{2} + {(\frac{\sqrt{3} k}{8})}^{2}} = \frac{\sqrt{7} k}{8}$

$E_{B} = \frac{k}{16}$

So, $\frac{E_{A}}{E_{B}} = 2 \sqrt{7}$

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