(i) Quantum theoretical methods have established themselves to explain natural phenomena in contemporary Physics. Comment. (ii) Formulate the axioms of quantum theory. (iii) State Born's condition on a wave function. What is its physical meaning?
Calculate the increase in entropy when 1 kg ice melts at zero degree centigrade. The Latent heat of fusion of ice is 3.36 \times 10^5\text{ joules/kg}. (Assume that the melting is an isothermal reversible process)
Obtain van der waals' equation of state for real gases. What is the value of critical coefficient for an ideal gas ? Show that the value of the critical coefficient for van der Waals' gas is independent of the type of gas.
How can one obtain a temperature and identify the elements in stellar bodies using Saha's thermal ionisation equation ?
Derive an expression for the Maxwellian distribution of velocities for the molecules of an ideal gas.
What value of inductance has to be used so that a lamp with rating of 200 volt and 10 Amperes lights the same way with 250 V source at 50 Hz.
From Planck's radiation law, derive Wien's displacement law and Rayleigh Jean's law.
Derive the energy continuity equation for electromagnetic waves using the poynting vector.
Define scalar and vector potentials. Recast Maxwell's equations in terms of these potentials.
What is gauge transformation? Define coulomb gauge. Derive the equation for vector potential under coulomb gauge.
Explain the use of a parallel resonance circuit
(i) as a rejector circuit
(ii) for current amplification.
An inductance is connected to 6 volt battery through a resistance R. What is the steady state current in the circuit? Alter what time the battery would be delivering one half its steady state current?
A conducting sphere of radius `a' is placed in a uniform electric field E_0. Using the method of images, show that the potential function is given by \phi = -E_0 \left(r - \frac{a^3}{r^2}\right) \cos \theta.
Calculate the electric field as a function of position due to a dipole whose potential is given by V = \frac{P \cos \theta}{4 \pi \epsilon_0 r^2} \quad \text{where } r = \sqrt{x^2 + y^2} The dipole is located at the origin of the x, y axis system.
Parallel rays fall on circular aperture of diameter 1 mm. At a certain position of the screen one gets a dark spot on an axial point. When the screen is moved by 12.5 cm, one again gets a dark spot. Determine \gamma (wavelength).
The phase velocity in a material is \sqrt{g/k} where k is the propagation constant. Prove that the group velocity will be half of the phase velocity.
Certain string has a linear mass density of 0.25\text{ kgm}^{-1} and stretched with a tension of 25 N. One end is given a sinusoidal motion, its frequency 5 Hz and amplitude 0.01 metre. If at t = 0, the end has zero displacement and is moving along the positive Y direction, derive the wave speed, the wavelength and the wave equation of the wave in the string.
Why does one get polarised light from a Nicol's prism? How should one adjust the polariser and analyser, so that an intensity of the incident light is reduced by a factor of 0.25?
A parallel laser beam is incident perpendicularly on a photographic plate. An object is placed at a distance a in front of the photographic plate. Discuss the recording from the plate. If the plate is illuminated by the same light, what is expected and why?
Monochromatic light from a distance source of wavelength \lambda falls on a double slit. A glass plate of thickness t is inserted between one slit and the screen. Calculate the intensity at the central point as the function of thickness t.
