1. Attempt any five parts: Two point charges Q1 and Q2 are 3 m apart and their combined charge is 20 IlC. If one point charge repels the other with a force of 0.075 what are the magnitudes of the two charges? The surface charge density of a flat sheet of area 50 cm^2 is An electron situated at a distance of 1·5 cm from the centre of the sheet experiences a force of 1·8 x 10^-12 N directed away from the sheet. Calculate the total charge on the sheet. Show that when a dielectric material is filled between the plates of a parallel plate capacitor, the value of capacitance increases by a factor the dielectric constant of the material. In a cyclotron, the diameter of the pole faces is 100 cm and the magnetic field between the pole faces is 0.60 tesla. The cyclotron is used for accelerating protons. Calculate the kinetic energy of protons in eV. In the Bohr model, the electron of a hydrogen atom moves in a circular orbit of radius 5·3 x 10^-11 m with a speed of 2.2 x 10^6 . Determine its frequency and current in the orbit. An electron of mass m moving around a nucleus in a circular path of radius r constitutes an atomic magnet. Obtain the relation between its magnetic moment and the angular momentum of the electron.
Define self-inductance and obtain the expression for self-inductance of a solenoid. The electric field of an electromagnetic wave in vacuum is given by <img src='./qimages/10407-1h.jpg'>

where E is in volts per metre, t is in seconds and x is in metres.
Determine the frequency, the wavelength, the direction of propagation and the direction of the magnetic field associated with the wave.

2. Attempt anyone part ABCD is a square of side 0·02 m. Charges of 16 x -16 x C and 32 x C are placed at points B and respectively. Determine the magnitude and direction of electric field at the point D. Discuss the effect of electric field on a dielectric. Deduce Gauss's law for a dielectric medium.

3. Attempt anyone part State Biot-Savart's law. Using this law, derive an expression for magnetic field along the axis of a current loop. Write one analogy and one difference between Coulomb's law and Biot-Savart's law. A long straight wire of radius 5.0 mm carries a current of 20 A. Calculate the magnetic field at the surface of the wire. Calculate the perpendicular distance from the axis of the wire at which the magnitude of the magnetic field will be half of its value at the wire surface.

(ii) The value of the magnetic field at the centre of an air core solenoid is 0.40 mT. If the current flowing in the solenoid is 0·4 calculate the number of turns per cm.

4. Attempt anyone part Define Lorentz force. A beam of electron
passes undeflected through two mutually perpendicular electric and magnetic fields. If the electric field is cut off and the same magnetic field is maintained, the electrons move in the magnetic field in a circular path of radius 2·2 em. Determine the ratio of the electronic charge to mass if the magnitude of electric field is 15 kVm^-1 and the magnitude of magnetic field is 2 x T. Write Maxwell's equations in differential form for vacuum with no source of charges or currents and deduce the wave equation. Also calculate the speed of electromagnetic waves.

Physical Constants: <img src='./qimages/10407-4b.jpg'>