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.
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.
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?
Explain the use of a parallel resonance circuit
(i) as a rejector circuit
(ii) for current amplification.
What is gauge transformation? Define coulomb gauge. Derive the equation for vector potential under coulomb gauge.
Define scalar and vector potentials. Recast Maxwell's equations in terms of these potentials.
Derive the energy continuity equation for electromagnetic waves using the poynting vector.
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.
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).
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?
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?
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.
Define scattering cross-section. A charged particle of mass m and charge Z_e is scattered by another charged particle of charge Z_e at rest. Deduce the expression for the scattering cross-section.
Determine equation of trajectory for a particle under central force `F', the magnitude of which is given by F = -\frac{A}{r^2} + \frac{B}{r^3} where A and B are positive constants.
A person in a spaceship is holding a rod of length of 0.5 m, the space ship is cruising at a speed V parallel to the earths surface. What does the person in the space ship notice as the rod is rotated from parallel to perpendicular to the space ships motion? What does an observer on earth's surface notice?
The mass of muon at rest is 207\text{ m}_e where m_e is the electron rest mass (0.511\text{ MeV}). The mean life time at rest for muon is 2.2\ \mu\text{s}. The life time of muon emerging from an accelerator is measured in the laboratory as 6.9\ \mu\text{s}. Estimate the speed of these muons in the laboratory.
A star of the size of our sun having a radius of 7 \times 10^5\text{ km} and having a mass 2 times as that of the sun is rotating at a speed of one revolution every 10 days. If the star undergoes a gravitational collapse to a neutron star of radius 10\text{ kms}, assuming that the star is a uniform sphere at all times, calculate the rotation speed of the neutron star. The moment of inertia of solid about its diameter is 2/5\text{ MR}^2 where M and R are the mass and radius of the solid sphere respectively.
Obtain the equation of motion of a particle moving relative to a rotating frame of reference. Explain the term representing coriolis force in this expression.
A system with 2 independent coordinates x_1 and x_2 has the following Larangian L = \frac{1}{2} \frac{(\dot{x}_1)^2}{\alpha + \beta x_2} + \frac{1}{2} (\dot{x}_2)^2 (x_2)^2 - \gamma x_2 \alpha, \beta, \gamma being constants. Obtain the Lagrangian equation of motion.
