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

To show that the magnetic field at a point due to a magnetic dipole is perpendicular to the magnetic axis when the line joining the point with the center of the dipole makes an angle of \( \tan^{-1}(\sqrt{2}) \) with the magnetic axis, we can follow these steps:

### Step 1: Define the angle
Let \( \theta \) be the angle between the line joining the point to the center of the dipole and the magnetic axis. Given that \( \theta = \tan^{-1}(\sqrt{2}) \), we can express this in terms of tangent:
\[ \tan \theta = \sqrt{2} \]

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