1. Attempt any five parts A small object carrying a charge of -5x C experiences a force of 20 x N in the negative x-direction when placed at a point in an electric field. What is the electric field at this point? What would the magnitude and direction of the force acting on a proton placed at this point be?
Hydrogen atom consists of an electron and a proton separated by an average distance of 5.3 X 10^-11 m. Calculate the electrical force between the electron and the proton and compare it with the gravitational force acting between them. Using Gauss's law, obtain an expression for electric field at a point inside a uniformly charged straight wire. Explain the polarisation of dielectrics placed in an electric field and hence define electrical susceptibility. Draw a labelled hysterisis curve for a ferromagnet. Explain the terms remanence and coercivity. The magnetic field at the centre of a solenoid of length 2·2 m and diameter 0·9 m is 0·4 tesla. Calculate the energy stored in the field of the coil. Consider an electromagnetic wave in empty space whose electric field is given by

E 40 x exp[-i(l0^8t

Determine the direction of propagation, wave number, frequency and the magnetic field of the wave.
Explain the working of electrolytic capacitors.

2. Attempt any one part
Derive an expression for electric field due to a dipole at a point along its axis; and a point on the perpendicular bisector of the dipole axis, Two rectangular plates of area of cross-section 6.45 x m^2 each are kept parallel to each-other in free space. The separation between them is 2 x m and a voltage of 10 V is applied across these plates. Calculate the capacitance. If a material of dielectric constant 6·0 is introduced in the region between the two plates, calculate capacitance and the electric displacement D.

3. Attempt any one part
Using Ampere's law, obtain the expression for the magnetic field due to a solenoid.

(ii) A solenoid has 2·0 x 10^3 turns per meter. If we wish to obtain a magnetic field of 8·0 x tesla, what should be the value of current in the solenoid? Show that the line integral of the electric field over a closed path. is equal to zero.

4. Attempt any one part
Explain the working· of a velocity selector.
The diameter of a cyclotron is 0·5 m and the magnitude of the magnetic field at its centre is 1·4 tesla. If this cyclotron is used for accelerating deuterons e and m 3·3 x 10^-27 calculate the cyclotron frequency and the kinetic energy of deuterons as it emerges from the cyclotron. Show that the electromagnetic field described by

<br><br> <img src='./qimages/12714-4b1.jpg'>

will satisfy Maxwell's equations in charge-free and current-free empty space if <img src='./qimages/12714-4b2.jpg'>

Physical Constants: <img src='./qimages/12714-4b3.jpg'>