(a) (i) A proton moving with velocity $\vec{V}$ in a non. uniform magnetic field traces a path as shown in the figure.

The path followed by the proton is always in the plane of the paper. What is the direction of the magnetic field in the region near points $P, Q$ and $R$ ? What can you say about relative magnitude of magnetic fields at these points?

(ii) A current carrying circular loop of area $A$ produces a magnetic field $B$ at its centre. Show that the magnetic moment of the loop is $\frac{2 B A}{\mu_0} \sqrt{\frac{A}{\pi}}$

OR

(b) (i) Derive an expression for the torque acting on a rectangular current loop suspended in a uniform magnetic field.

(ii) A charged particle is moving in a circular path with velocity $\vec{V}$ in a uniform magnetic field $\vec{B}$. It is made to pass through a sheet of lead and as a consequence, it looses one half of its kinetic energy without change in its direction. How will (1) the radius of its path (2) its time period of revolution change?