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A small electric dipole $\vec{p} = p \hat{i}$ is placed at the origin and electric field at point at A (x,0) is found to be E. Now the dipole is rotated in anti clockwise in XY plane about Z- axis through an angle of 60⁰. Then electric field at the same point will be.

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$\frac{E}{4}$

$\frac{\sqrt{3 E}}{4}$

$\frac{\sqrt{5 E}}{4}$

$\frac{\sqrt{7 E}}{4}$

answer is D.

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Detailed Solution

In the first case, $E = K \frac{2 p}{x^{3}} \Rightarrow \frac{E}{2} = \frac{k . p}{x^{3}}$
In the second case $E^{1} = \frac{k . p}{x^{3}} \sqrt{3 \cos^{2} 60^{o} + 1} = \frac{\sqrt{7} E}{4} .$

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