Q: A charge of 1 C is placed at one end of a non conducting rod of length 0.6 m. The rod is rotated in a vertical plane about a horizontal axis passing through the other end of the rod with angular frequency 10^{4} π rad/s. Find the magnetic field at the point on the axis of rotation at a distance of 0.8 m from the centre of the path.

Sol: $\large B = \frac{\mu_0}{4\pi} \frac{2\pi i r^2}{(r^2 + x^2)^{3/2}}$

As $\large i = \frac{q \omega}{2 \pi}$

$\large B = \frac{\mu_0}{4\pi} \frac{2\pi q \omega r^2}{2 \pi(r^2 + x^2)^{3/2}}$

$\large B = \frac{\mu_0}{4\pi} \frac{q \omega r^2}{(r^2 + x^2)^{3/2}}$