Write down Maxwell's field equations for free space and obtain expressions for velocity of electromagnetic waves.

Two particles carrying 4C and -2C charges are placed on a 1 m long straight wire. Determine the point on the line joining these particles where the electric potential is zero with reference to the positively charged particle

Explain with the help of diagrams what spherically and cylindrically symmetric charge distributions are. What is the electric field at a point inside a hollow metallic sphere of radius R having volume charge densityp?

Note: Attempt all questions. The marks for each question are indicated against it. Symbols have their usual meanings. 1. a) Determine the electrostatic force and electrostatic field on a charged particle located at A in the Figure given below due to the charged particles situated at B and C. The value of the charge on each of these particles is indicated in the Figure.

Express your result both in the unit vector notation and as magnitude. 

Derive Planck’s law of blackbody radiation using Bose-Einstein statistics. Using this law, obtain (i) Rayleigh-Jeans Law and (ii) Wien’s Law.

Gibbs paradox.

Bose-Einstein condensation.

Establish van der Waals’ equation of state for a real gas. Plot van der Waals’ equation of state on p-V diagram.

Define mean free path of a molecule in a gas. Derive the law of distribution of free paths. 

Calculate the temperature at which the root mean square speed of hydrogen and oxygen molecules will be equal to their escape velocities from the earth's gravitational field. The radius of the earth is 6400 km.

Take N_A=6x10²⁶ mol^-1, g-9.8ms^-2, kg-1.38x10²³JK^-1

List the differences between first and second order phase transitions. What are the characteristics of lambda transition? 

Using Maxwell's relations, derive the first and second energy equations. 

The modulus of rigidity of a wire is

The following measurements are made for L, r and  / N

r = 1.5  0.05 mm

L = 400  2 mm

 = 6.00  0.20 rad N^-1 m^-1

Obtain the best value of .

The efficiency of a Carnot engine is 30%. Its efficiency is to be raised to 60% By how much must the temperature of the source be increased if the sink is at 27°C? 

A website has on the average two hits per hour. Assuming a Poisson distribution for the number of hits per hour (X), calculate the probability that there are at most three hits.

Draw a Carmot cycle on p- diagram. Show that the amount of heat absorbed (rejected) in a reversible cycle is proportional to the temperature of source (sink).

Using the first law of thermodynamics for an adiabatic process, establish the relation PV=K, where y is the ratio of heat capacity at constant pressure to that at constant volume. Plot this equation on a p- diagram. What will be its slope?

Derive an expression for the work done by a gaseous system for an isothermal expansion of an ideal gas. 

Explain the working of a platinum resistance thermometer with the help of a neat and labelled diagram.

An athlete is running in four races and in each race she has a 60% chance of winning. What is the probability that she will win at least two races?