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A small electric dipole is placed at origin with its dipole-moment directed along positive x-axis. The direction of electric field at point $\left( {2,\,\,2\sqrt 2 ,\,\,0} \right)\$ is

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along z-axis

along y-axis

along negative y-axis

along negative z-axis.

answer is B.

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Detailed Solution

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$\tan \theta = \frac{y}{x} = \frac{{2\sqrt 2 }}{2} = \sqrt 2 \$

$\cot \theta = \frac{1}{{\sqrt 2 }}$

$\tan \phi = \frac{{\tan \theta }}{2} = \frac{{\sqrt 2 }}{2} = \frac{1}{{\sqrt 2 }} = \cot \theta \$

Now, $\left[ {\tan \phi = \frac{{{E_0}}}{{{E_r}}} = \frac{{\tan \theta }}{2}} \right]\$

then $\phi = 90^\circ - \theta \$

i.e. $\vec E\$ is along +ve y-axis

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