First slide

Electric dipole

Question

An electric dipole is placed at the origin O and is directed along the x-axis. At a point P, far away from the dipole, the electric field is parallel to y-axis. OP makes an angle $θ$ with the x-axis, then

Moderate

A

$tanθ = \sqrt{3}$
B

$tanθ = \sqrt{2}$
C

$θ = 45 °$
D

$tanθ = \frac{1}{\sqrt{2}}$

Solution

We know that in this case electric field makes an angle $θ$ + a with the direction of dipole.
$Also, tanα = \frac{1}{2} tanθ Here, θ + α = 90 ° \Rightarrow α = 90 ° - θ Hence \tan (90 ° - θ) = \frac{1}{2} tanθ \Rightarrow cotθ = \frac{1}{2} tanθ \Rightarrow \tan^{2} θ = 2 \Rightarrow tanθ = \sqrt{2}$

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