Electromagnetic theory - Physics Previous Year Questions

The magnetic field (in A m⁻¹) inside a long solid cylindrical conductor of radius a = 0.1 m is, \(\vec{H} = \frac{10^3}{r}\left[\frac{1}{\alpha^2}\sin(\alpha r) - \frac{r}{\alpha}\cos(\alpha r)\right]\hat{\phi}\), where \(\alpha = \frac{\pi}{2a}\). What is the total current (in A) in the conductor?

Two magnetic dipoles of magnitude \( m \) each are placed in a plane as shown.
The energy of interaction is given by

In a constant magnetic field of 0.6 Tesla along the z direction, find the value of the path integral $\oint \vec{A} \cdot d\vec{l}$ in the units of (Tesla m$^2$) on a square loop of side length $(1/\sqrt{2})$ meters. The normal to the loop makes an angle of $60^\circ$ to the z-axis, as shown in the figure. The answer should be up to two decimal places. __________.