Show that the magnetic field at a point due to a magnetic dipole is perpendicular to the magnetic axis if the line joining the point with the centre of the dipole makes an angle of `tan^(-1) (sqrt(2))` with the magnetic axis.

Explanation

Let magnetic field at a point makes an angle `alpha` with the line joining the point and centre of the magnet then
`tan alpha = 1/2 tan theta ` ...........(1)
Where `theta` is angle between line joining the point and centre of magnet with magnetic axis. If magnetic field is perpendicular to axis then `theta + alpha = 90^@ rArr alpha = 90 - theta ` .
On substituting in equation (1) we get the following:
` tan (90^@ - theta) =1/2 tan theta `
` rArr cot theta =1/2 tan theta `
` rArr tan^2 theta = 2`
` rArr tan theta = sqrt2`
` rArr theta = tan^(-1) (sqrt2)`