State Planck's formula for black-body spectrum. Show that 'Planck's formula reduceds to Wien's formula at short wavelengths,

Write down Maxwell's equations for an isotropic homogenous dielectric and point out their relations with observational laws. How do the equations lead to the concept of electromagnetic waves?

Show that the temperature (T) of a plant varies inversely as the square root of its distance (R) from the Sun. (The Sun and Planets are considered to be black-bodies in radiative equilibrium.)

State Biot-Savart's law. Derive an expression for the magnetic field at points along the axis of a circular coil.

In a nuclear explosion, the maximum temperature reached was of the order of 10^8\text{ K}. Estimate the order of wavelength at which the maximum of radiated energy occurs.

If steady voltage is applied to an L-R circuit, show how voltage across the inductance and the current in the circuit changes with time. Explain the term inductive time constant.

The total energy, U in oscillating L-C circuit is given by: U = U_B + U_E = \frac{1}{2} L i^2 + \frac{1}{2} \frac{q^2}{C} When the resistance of the circuit is zero From this show that it is an oscillatory circuit and find the time period.

Write a short note on Uniqueness theorem in electrostatics.

Write down Plank's law of radiation and establish Wien's law from it.

Set up the equation for the discharge of capacitor C connected in series with a resistor R and an inductor L. If R_0 stands for 2(L/C)^{1/2}, discuss three cases: R < R_0, R = R_0 \text{ and } R > R_0 What will you observe if the discharge takes place at low temperature when the material of resistor has become superconducting?

Alpha particles of velocity v enter a uniform magnetic field in perpendicular direction. If electrons of the same velocity v enter the same magnetic field the same way compare: (i) the curvatures of their path and (ii) the tracks they would show in (say) a bubble chamber.

Show that the electric field intensity due to any distribution of charges at rest can be expressed as the gradient of a potential. What is the relation between potential and potential energy? A thin disc of radius R is uniformly charged, \sigma being the charge per unit area. Find the potential and the electric intensity at points on the axis of the disc. How do these change as one crosses the disc? Explain the changes physically.

Two charges are placed at a distance of 1 metre. The magnitude of one charge is double that of the second charge. Find the neutral points in the two cases: (i) the charge are of the same sign (ii) the charge are of opposite sign. What happens to the neutral point if the two charges are of equal magnitude and opposite sign?

In certain region of space in vacuo, the components of the magnetic induction are (in weber per square meter) B_x = A e^{-ay} + bx B_y = A c^{-ax} + cy B_z = 0 where x, y, z, are in metres and A, a, b and c are constants. Find the relation, if any between these constants and also the current distribution that gives rise to this field. (No electric field is present). Is the current distribution consistent with the charge conservation principle?

Define solar constant and say which of the values 1.34\text{ W/m}^2, 1.34 \times 10^3\text{ W/m}^2, 1.34 \times 10^5\text{ W/m}^2 is valid for it. Calculate the total energy radiated by the sun in one second and hence the decrease in its mass per second.

A circular coil of wire having 100 turns and radius 10 cm is rotating about a vertical axis in its own plane uniformly at rate of 480 revolutions per minute. There is a horizontal magnetic field of intensity 0.01\text{ Wb/m}^2. The terminals of the coil are connected to the ends of an inductor having inductance 0.01 henry. Assuming that the resistance in the circuit can be neglected, find the current in the circuit at the instant the plane of the rotating coil is perpendicular to the magnetic field.

A charged particle moving horizontally towards the east with a velocity of 10^{5}\text{ m/s} enters into a region where there is a horizontal electric field E intensity 100\text{ volt/cm} directed towards the north as also a magnetic field B. The particle continues to move in the same direction as before. What can you san about the field B? Is it completely determined? What will be the path, of particle if the magnetic Field be switched off?

Write a brief scientific note on Ferrimagnetism and ferrites.

Starting from Biot-Savart law, calculate the magnetic field at the centre of a solenoid of length 1 meter, radius 2 cm and having 25 turns per centimeter, the current through the solenoid being 1 ampere.

The components of an electrostatic field in vacuo are given as E_x = \frac{a}{r^3} + \frac{bx^2}{r^5} E_y = \frac{cxy}{r^5} E_z = \frac{fxz}{r^5} where a,b,c, and f are constants x,y,z, the rectangular cartesian coordinates and r^2=x^2+y^2+z^2. Using the basic equations obeyed by the electrostatic field in vacuo, find he relations between a,b,c and f and determine the charge density at a general point in space. Would that explain the observed field?