UPSC Physics Optional PYQs (CSE & IFoS)PYQs

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 radio station transmits electromagnetic waves isotropically with an average power of 200\,\mathrm{kW}. Determine the average magnitude of the maximum electric field at a distance of 5\,\mathrm{km} from it.

A plane electromagnetic wave propagating along +\hat{z} direction is incident normally on the boundary at z=0 between medium A(z<0) and medium B(z>0). Determine the reflection coefficient and transmission coefficient for the wave.

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?

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?

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}.

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

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.

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.

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.

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.

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.

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

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).

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.

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.

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.

Find out the angle between the reflected and refracted rays when a parallel beam of light is incident on a dielectric surface at an angle equal to the Brewster's angle. Explain how do you use this concept to produce linearly polarized light.