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

Given `0 = tan^(-1)sqrt(2)`
`rArr tan theta = sqrt(2) rArr 2 = tan^(2)theta `
`rArr tan theta = 2 cos theta `
`rArr (tan theta )/(2) = cot theta`…(i)
We know `(tan theta )/(2) = tan alpha`..(ii)
From (i) and (ii) we get
`tan alpha= cot theta`
`or tan alpha = -tan(90 - theta)`
`or alpha = 90 - theta `
`or theta + alpha = 90^(@)`
Hence magnitic field due to the dipole i9s perpendicular to the magnitaic axis