Question

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(√2) with the magnetic axis

Answer 1

Given :

θ = tan^–1√2  => tanθ = √2 => 2 = tan²θ

=> tanθ = 2cotθ => tanθ/2 = cotθ

We know tanθ/2 = tanα

Comparing we get, tanα = cotθ

or, tanα = tan(90 – θ) or α = 90 – θ or θ + α = 90

Hence magnetic field due to the dipole is ⊥r to the magnetic axis.