Write a short note on Wien's Law.

Write down Maxwell's equations in vacuum. Show that in the source-free case, both the electric and magnetic vectors obey wave equations of identical form and considering a plane wave solution, prove dial the electric and magnetic vectors and the direction of propagation are mutually perpendicular. Show further that there is a propagation of energy given by the Poynting vector.

Three point charges are situated at the vertices of an equilateral triangle (one at each vertex); Show that the electric intensity vanishes at the centroid if and only if the charges are equal in magnitude and of the same sign.

Two point charges each of magnitude +2\text{ millicoulomb} are at A and B in front of a infinite conducting plane which is grounded. The line OAB is the perpendicular to time plane with the point O on the plane. If \mathrm{OA}=1\text{ m} and \mathrm{OB}=2\text{ m} calculate the force on the charge at A

An electromotive force p_0 \sin pt + E_1 \sin 2 pt is impressed on a circuit containing an inductor and a resistor. Set up the differential equation obeyed by the current and show that in the steady state the current comprises two sinusoidal terms. Calculate the average power dissipation in the circuit. What is the difference, if any, between a varying current and an alternating current?

A wire of length l is bent into the form of a rectangle of side a and b and carries a current I. Calculate the magnetic field intensity at the centre of the rectangle. Show further that the intensity is minimum for a = b.

Derive an expression for the Poynting's vector and explain us significance A light source (one kilowatt) is radiating energy uniformly. Determine the intensity of the electric field at a distance of one metre from the sources.

Write down the expression for energy distribution of a black- body radiation at temperature T and deduce Wien’s displacement law.

A 220\text{ volt}, 50\text{ cycle}, supply is connected to a circuit containing a resistance of 20\text{ ohms} in series with a 100\mu\text{F} capacitor. Determine the current and the phase.

A singly charged positive ion is accelerated through a potential difference of one \text{kV}, and the ion passes through a uniform magnetic field of B=0.2\text{ Wb/m}^{2} and consequently gets deflected through a circular path of radius 0.1\text{ metre}. Find out the mass number of the ion.

State Kirchoff's laws for the distribution of currents (a) in the usual form for steady currents and (b) in a form applicable to alternating current networks. Discuss the method for comparing inductances by using Maxwell's bridge. State the disadvantages of the method.

Discuss briefly the various ways of modulation of electromagnetic waves for the purpose of communication through radio and television.

Write a note on Anomalous dispersion.

Obtain an expression for the force exerted on unit volume of a paramagnetic substance in a non-uniform magnetic field. How could you experimentally distinguish and diamagnetic and paramagnetic substance?

Write down Maxwell s equations for the electromagnetic field in Free space and show that \vec{E} satisfies the wave equation. Hence obtain the expression for the velocity of e.m. waves in free space.

Derive an expression for the mean energy \varepsilon of a Planck oscillator in thermal equilibrium with the surroundings. How does the ratio h\nu / kT vary as the temperature T varies from \leqslant h\nu / k to \leqslant h\nu / k, the symbols having the usual meanings?

What is dielectric susceptibility? Describe how you can determine the radius of an atom from the measurement of the dielectric constant of a gas. A parallel plate condenser consists of two plates of area 400\text{ sq. cm.} each separated by a sheet of material of 0.10\text{ mm} thickness. Find the capacity in microfarads when the dielectric constant of the material is 5.0.

In an oscillatory circuit L = 0.30\text{ henry} and C = 1.2 \times 10^{-6}\text{ F,} determine the value of maximum resistance so that the circuit may remain oscillatory.

The parallel plates of a capacitor have an area of 2000\text{ cm}^2 each and are 1\text{ cm} apart. They are originally at a potential difference of 3,000\text{ volts}. When a dielectric is introduced covering the whole space between the plates, the potential difference becomes 1000\text{ volts}. Calculate the capacitance of the capacitor before and after insertion of the dielectric. What is the dielectric constant of the dielectric?

Two homogeneous isotropic dielectric media have a common plane boundary and ale otherwise infinite in extent. An electromagnetic wave is incident on the boundary. Establish the laws of reflection and refraction.