PYQ Bank

Show that energy stored in a capacitor is \frac{1}{2} \frac{q^2}{C} while the energy stored in the inductor is \frac{1}{2} L i^2, where the symbols have their usual meaning.

Calculate \omega_0 \Delta \omega and quality factor Q for LCR parallel resonant circuit given the values C = 0.4 \muF, L = 4 mH and R = 1 K\Omega.

Show that it is possible to arrive at Stefan-Boltzmann law with the aid of Carnot's cycle using black body radiation as the working substance.

If the avenge distance between the sun and earth is 1.5 \times 10^{11} m, find the avenge solar energy flux and the earth (solar constant) given the power radiated by the sun = 3.8 \times 10^{26} watt.

Give the four basic experimental laws of electro magnetics in words and in mathematical form. Explain how they are modified to obtain the Maxwell's equations. Show how these equations lead to prediction about the speed at which e.m. waves are propagated in vacuum.

An excess charge placed on an insulated conductor, resides entirely on its outer surface. Priestly checked his observation and showed that the inverse square law of force followed from it. Explain.

A series circuit consisting of 410\text{ ohms} of resistance, 81.0\ \mu\text{H} of inductance and 225\ \mu\mu\text{F} of capacitance is excited by a constant voltage amplitude generator of variable frequency. At what frequency is the maximum power delivered?

A harmonic emf is applied to a series circuit containing resistance, inductance and capacitance. Derive the expression for the current and condition for resonance.

What Poynting vector ? Explain how the transport of electromagnetic energy is expressed quantitatively by Poynting vector.

State Coulomb's law and show that the electric field can be derived from a potential function. If the charge distribution is continuous, find the integral formula for determining its field.

Write a short note on Uniqueness theorem in electrostatics.

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.

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

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.

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

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?

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?