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

Explanation:

To Prove: 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.

Given data in the question  

Angle made by point of observation P with dipole axis,

     $\theta=\tan ^{-1} \sqrt{2}$

$\tan \theta=\sqrt{2}$

     $2=\tan ^{2} \theta$

$\tan \theta=\cot \theta$

$\frac{\tan \theta}{2}=\cot \theta \quad \ldots e q^{n} 1$

We know,

$\frac{\tan \theta}{2}=\tan \alpha \quad \ldots \cdot e q^{n} 2$

We get to compare (1) and (2)

$\tan \alpha=\cot \theta$

$\tan \alpha=\tan (90-\theta)$

     $\alpha=90-\theta$

$\theta+\alpha=90^{\circ}$

The magnetic field is therefore perpendicular to the magnetic axis, owing to the dipole.