(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?

(a) (i) (1) What are coherent sources? Why are they necessary for observing a sustained interference pattern?

(2) Lights from two independent sources are not coherent. Explain.

(ii) Two slits 0.1 mm apart are arranged 1.20 m from a screen. Light of wavelength 600 nm from a distant source is incident on the slits.

(1) How far apart will adjacent bright interference fringes be on the screen?

(2) Find the angular width (in degree) of the first bright fringe.

OR

(b) (i) Define a wave front. An incident plane wave falls on a convex lens and gets refracted through it. Draw a diagram to show the incident and refracted wave front.

(ii) A beam of light coming from a distant source is refracted by a spherical glass ball (refractive index 1.5) of radius 15 cm . Draw the ray diagram and obtain the position of the final image formed.