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 `theta` with the `x`-axis then
A. `tan theta =sqrt(3)`
B. `tan theta =sqrt(2)`
C. `theta= 45^(@)`
D. `tan theta= (1)/(sqrt(2))`

Answer 1

Correct Answer - b
As we know that in this case electric field makes an angle `theta+alpha` with the direction of dipole

Where `tan alpha= 1/2 tan theta`
Here `theta+alpha= 90^(@)implies alpha= 90^(@)-theta`
Hence `tan(90^(@)-theta)= 1/2 tan thetaimplies cot theta= 1/2 tan theta`
`implies tan^(2) theta= 2implies tan theta = sqrt(2)`