What are the vector and scalar potentials ? Derive Maxwell's wave equations in terms of these potentials.

What do you understand by a perfect black body? Can it be realised in practice ? Show that the ratio of the emissive power to the absorptive power for all bodies at a given temperature is equal to the emissive power of a perfectly black body.

Given the temperature of the Sun's surface T = 5755\text{ K}, radius of the Sun 6.9 \times 10^5\text{ km}, distance between the Earth and the Sun 1.5 \times 10^8\text{ km}. Estimate the solar constant (i.e. the energy received per sec per unit area of the Eath's surface). Assume \sigma = 5.7 \times 10^{-8}\text{ W/m}^2\text{-K}^4.

Show that the Poynting vector \bar{S} = (\bar{E} \times \bar{H}) represents the energy flow per unit area per unit time both in magnitude and direction in case of a plane electromagnetic wave.

Find out the magnetic field inside a long solenoid carrying current i and having n turns per unit length.

A point charge q is held at a distance d in front of an infinite grounded conducting plane. What is the electric potential in front of the plane ?

A network PQRS is connected as shown in the figure below. Apply Kirchhoff's law and show that the current flowing through the 20\ \Omega resistor PR is 0.029 A.

What is the volume density of the charge in a region of space, where the electrostatic potential is given by V = a - b (x^2 + y^2) - c \ln (x^2 + y^2), where a, b, c are constants ?

Define the strength of a magnetic shell and calculate the magnetic potential at any neighbouring point due to this shell. Does the potential depend on the shape of the shell ?

Define Poynting vector and explain its significance. The electric field vector for an electromagnetic field travelling in vacuum is given by \vec{E} = E_0 \cos (kz - \omega t) \hat{i} Calculate the Poynting vector for the wave and show that its magnitude is equal to the energy density of the wave time the velocity of light.

{cse-q-3-223-fig-1} A parallel LC circuit is operated at a frequency \omega, which is less than the resonant frequency \omega_0 of the LC circuit. Explain whether the reactance is inductive or capacitive.

Show that a sprining nucleus precesses in a magnetic field. Explain the underlying principle of NMR spectroscopy. The magnetic moment of a position is 2.793 \mu\text{ N}. Calculate the radio frequency at which nuclear magnetic resonance occurs in water kept in a magnetic field of T.

{cse-q-3-219-fig-1} A bridge network with resistance, capacitance and inductance is given in the above figure. Show that the conditions for balancing the bridge are independent of the frequency of applied voltage.

A cylinder of length L and radius b has its axis coincident with z-axis. The electric held in th region is E = 100 k. Find the electric flux through (i) the top circular end (ii) the bottom circular end (iii) the curved wall of the cylinder (iv) the closed surface of the cylinder

Consider an infinite grounded conducting plane. If a point charge is held at a distanced d from the plane, compute by method of images, the electric potential above the plane and the induced charges on the conductor.

What is Laplace equation ? Determine the average electric potential over a spherical surface, due to a point charge q placed at a distance r from the centre of the sphere. Assume r to be greater than the radius of the sphere.

Earth receives 1.3\text{KW/m}^2 of radiant energy from the Sun. Assuming Sun to be a spherical black body of radius 7 \times 10^8\text{m} and Earth-sun distance to be 1.5 \times 10^{11}\text{m}, Calculate the surface temperature of Sun. (Stefan-Boltzmenn constant \sigma = 5.67 \times 10^{-8}\text{ Wm}^{-2}\text{K}^{-4}).

A plane wave of frequency \omega, which into two linear dielectric media. It has a normal incidence at the interface of the media. Giving appropriate for the intensities of reflected and transmitted rays.

A series LCR circuit with \mathrm{L} = 2\text{ H}, \mathrm{C} = 2\text{ }\mu\text{F} and \mathrm{R} = 20\\ \Omega is powered by a source of 100\text{ volts} and variable frequency. Find

(i) the resonance frequency, f_0,

(ii) the value of Q

(iii) the width of resonance \Delta f and

(iv) the maximum current at resonance.

Why did Maxwell have to introduce the idea of displacement current? Derive the wave equation from Maxwell's laws. Obtain Fresnel's formula for reflection and transmission coefficients of the electric vector when it is perpendicular to the plane of incidence.