PYQ Bank

Discuss the principle of adiabatic demagnetization process to achieve low temperatures. Determine the fall in temperature produced by adiabatic demagnetization of a paramagnetic material at initial temperature of 3\ \mathrm{K} when the magnetic field is switched off from 10{,}000 oersted to zero. Given: heat capacity at constant magnetic field =0.2\ \mathrm{J\ g^{-1}\ K^{-1}} and Curie constant per gram mole per \mathrm{cm^3} =0.042\ \mathrm{erg\ K^{-1}\ g^{-1}\ Oe^{-2}}.

State the first law of thermodynamics for a diffusively interacting system. The temperature of 10\ \mathrm{g} of air is raised by 2^\circ\mathrm{C} at constant volume. Calculate the increase in its internal energy. Given: C_v=0.172\ \mathrm{cal\ g^{-1}\ ^\circ C^{-1}}.

What is a transformer? Is it for a.c. or d.c.? With a suitable diagram and representative symbol, explain the construction and necessary terms used in a transformer.

Calculate the magnitude of Poynting vector at the surface of the Sun. Given that the power radiated by the Sun = 3{\cdot}8 \times 10^{26}\text{ watts} and the radius of the Sun = 7 \times 10^8\text{ m}.

Write the equation for total scattering cross-section for electromagnetic waves. Under what condition the scattering is known as Rayleigh scattering? Write the importance of Rayleigh scattering in nature.

Show that the energy density in electrostatic field is given as u = \frac{1}{2} \bar{D} \cdot \bar{E} Further, show that the dielectric constant is a symmetric tensor except when the field energy vanishes identically.

Write expressions for divergence and curl of an electrostatic field. From these, obtain Poisson and Laplace equations. Two concentric conducting spherical shells having radii r_1 and r_2 (r_1<r_2) are charged to potentials V_1 and V_2, respectively. What are the electric potential and hence electric field in the space between the shells? Also find the charge on the inner shell.

For the electric field given by E=E_0e^{i\omega t}, show that the conduction current is in phase with the electric field, while the displacement current leads the electric field by \frac{\pi}{2} radians. Also, show that the displacement current in a good conductor is negligible compared to the conduction current at any frequency lower than the optical frequencies (f<10^{15}\ \mathrm{Hz}).

Write Maxwell's equations in free space in both differential and integral forms. Obtain wave equations and show that electromagnetic waves can travel in free space with a speed of light. Can one get the wave equations from the integral form of the Maxwell's equations?

A vertically oriented electric dipole having dipole moment \vec{p} is kept at height h above an infinitely large horizontal conducting plate, which is grounded as shown in the diagram. Calculate the force between the electric dipole and the conducting plate by using method of images.

Based on the hysteresis loops for soft iron and steel as shown in the diagram, which material would you prefer to utilise for making transformer cores and why?

Describe the oscillations of electric and magnetic fields in an ideal LC circuit. The applied voltage phasor in a circuit is (4+3i) volt and resulting current phasor is (3+4i) ampere. Draw the phasor diagram. Determine the impedance of the circuit and indicate whether it is inductive or capacitive in nature. Also find the power dissipation in the circuit.

Define a perfect blackbody. State Kirchhoff's law of radiation. What are the limitations of Kirchhoff's law?

A historic failure of Classical Physics is its inability to describe the electromagnetic radiation emitted from a black body. Consider a simple model for an ideal black body consisting of a cubic cavity of side L with a small hole on one side. Assuming the classical equipartition of energy, derive an expression for the average energy per unit volume and unit frequency range. In what way does this result deviate from actual observation? What is this law called?

Repeat the calculations now using quantum idea to obtain an expression that properly accounts for the observed spectral distribution. Find the temperature dependence of the total power emitted from the hole.

In a certain cyclotron, the maximum radius that the path of a deuteron may have before it is deflected out of the magnetic field is 20\,\mathrm{cm}.

(i) Calculate the velocity of the deuteron at this radius.

(ii) What is the energy of deuteron in \mathrm{MeV}? Given, magnetic field =1500 gauss and mass of deuteron =3.34\times10^{-27}\,\mathrm{kg}.

In what way Maxwell's concept towards electric field and magnetic field is different from Faraday's concept? Derive magnitude of displacement current in a parallel-plate capacitor and account it for the continuous path for the charges across the capacitor.

Derive Poisson's equation. Under what conditions it takes the form of Laplace's equation? If \phi_1, \phi_2, \cdots, \phi_n are solutions of Laplace's equation, then show that \phi = \lambda_1 \phi_1 + \lambda_2 \phi_2 + \cdots + \lambda_n \phi_n is also a solution. Here \lambda\text{s} are arbitrary constants.

What are ferromagnetic materials? By suitable figure, illustrate magnetic domain and magnetization curve for a ferromagnetic material.

Each square meter of the Sun's surface radiates energy at the rate of 6{\cdot}3 \times 10^7\text{ J/m}^2\text{ /s} and Stefan constant is 5{\cdot}669 \times 10^{-8}\text{ W/m}^2\text{ /K}^4. Find the temperature of the Sun's surface. Assume that the Stefan's law applies to the radiation.

Using the two-fluid model of a conductor (normal and superconducting) and the Maxwell's equations, derive the two London equations of superconductivity.