PYQ Bank

Derive the equation that represents Poynting's theorem. What is its physical significance?

What are the characteristic features of Rayleigh scattering? A very thin monochromatic beam of light is incident on a particle. Suggest a simple experimental method to ascertain whether the scattering by the particle is of Rayleigh type.

Prove that the work done on the charges by the electromagnetic force is equal to decrease in energy stored in the field, less the energy that flowed out through the surface. Explain what you mean by the Poynting vector.

Two spheres A and B having same temperature T are kept in the surroundings of temperature T_0. Consider T > T_0. The spheres are made of same material but have different, radii r_A and r_B. Using Stefan - Boltzmann distribution, determine which of these will lose heat by radiation faster.

Using Planck's radiation law, deduce Wien's displacement law. How does this law enable one to estimate the surface temperature of the Sun or a star?

Discuss the physical significance of Planck's radiation law in the context of emergence of New Physics. If the blackbody energy density u(\omega) has a functional dependence like u(\omega) \propto x^3 (e^x - 1)^{-1}, where x = \frac{\hbar\omega}{kT}, derive Wien's displacement law and comment on its importance.

Calculate the strength of the magnetic field to bring a proton nucleus and a ^{13}\text{C} nucleus to resonate at this frequency. Magnetic moment of \text{proton} = 2\cdot 7927\ \mu_\text{N} and magnetic moment of ^{13}\text{C} = 0\cdot 7022\ \mu_\text{N}. The NMR instrument operates at 30\cdot 256\text{ MHz}.

A plane conducting circular wire loop lies perpendicular to a uniform magnetic field B and its area S(t) is changed as S(t) = S_0 (1 - \alpha t), where 0 < t < \frac{1}{\alpha} (S_0 and \alpha are constants). The wire has resistance per unit length \rho\,\Omega\text{ m}^{-1}. Find the induced current through the wire. If the current in a certain coil varies at a rate of 50\text{ A s}^{-1}, the induced e.m.f. is V = 20\text{ volts}. What is the inductance of the coil?

Using Ampere's law, derive the magnetic field of a toroid (N turns each carrying current I) of inner radius a and outer radius b at a distance r midway between a and b.

The electric potential of a grounded conducting sphere of radius a in a uniform electric field E = E_0\hat{z} is given as \phi(r, \theta) = -E_0 r \left[ 1 - \left( \frac{a}{r} \right)^3 \right] \cos\theta Find the expression for the surface charge density on the sphere.

In a simple AC circuit involving only a resistor R = 50\,\Omega and a voltage source V, find the linear frequency of the generator if V = 0 \cdot 5\,V_m (V_m is peak e.m.f.) at time t = \frac{1}{720}\text{ s} (assuming V = 0 at t = 0).

Which of the Maxwell equations imply that there are no magnetic monopoles? Explain how the equations would get modified if magnetic monopoles would exist.

Verify whether the electric potential V = 15 x^2 y z - 5 y^3 z satisfies Laplace's equation or not.

In the circuit given below, find the values of currents I_1, I_2 and I.

A series RLC circuit has R=2\Omega. The energy stored in the circuit decreases by 1\% per period of oscillation. Its natural undamped frequency is 2\,\mathrm{kHz}. Determine the values of inductor L and the quality factor.

A series RLC circuit has a resistance of 100\Omega and an impedance of 210\Omega. If this circuit is connected to an a.c. source with an r.m.s. voltage of 220\ \mathrm{V}, how much is the average power dissipated in the circuit?

A conducting sphere of radius 5\,\mathrm{cm} has a total charge of 12\,\mathrm{nC} uniformly distributed on its surface in free space. Determine the displacement vector \vec{D} on its surface and outside at a distance r from the centre of the sphere.

Viewing ionosphere as a dielectric medium of refractive index \mu = \sqrt{1 - \omega_p^2 / \omega^2}, \omega_p being known as the plasma frequency, determine the group velocity of a radio wave of frequency \omega = \sqrt{2}\omega_p.

Under one-dimensional configuration, the charge density is given by \rho(x)=\dfrac{\rho_0x}{5}, where \rho_0 is a constant charge density. If the electric field \lvert\vec{E}\rvert=0 at x=0 and potential V=0 at x=5, determine V and \lvert\vec{E}\rvert.

Deduce an expression for resolving power of a diffraction grating, explaining its meaning. What will be the value of the number of slits in the grating to resolve \text{D}_1 and \text{D}_2 lines of sodium in the first order, assuming \lambda and \Delta\lambda respectively as 600\text{ nm} and 0\cdot6\text{ nm}?