UPSC Physics Optional PYQs (CSE & IFoS)PYQs

A long solenoid of radius R and n turns per unit length carries a sinusoidal current I = I_0 \cos \omega t. Determine the magnitude of induced electric field (E) outside the solenoid.

For an arbitrary localised charged distribution, obtain an expression of electrostatic potential V in terms of multipole expansion.

State Biot-Savart law. Calculate the magnitude of axial magnetic induction due to a circular loop of area A carrying current I.

Consider in the region 0 \le z \le 1\text{ m} an infinite slab made of a material with relative permeability, \mu_r = 3\cdot 5. If \vec{B} = (2y\hat{i} - 5x\hat{j}) \times 10^{-3}\text{ Wb/m}^2 within the slab, determine magnetisation \vec{M}.

A series R\text{-}L\text{-}C circuit is connected across a voltage source V = 100 \sin 300t. If R = 500\ \Omega, L = 1\text{ H} and C = 2\ \mu\text{F}, calculate the average power delivered to the circuit.

A cylindrical conductor is carrying a current along its axis which is assumed to be in z-direction. The current is uniformly distributed throughout its cross-section. Show that the vector potential \vec{A} associated with the magnetic induction due to the current-carrying cylindrical conductor is independent of z.

Distinguish between high dispersive power and high resolving power.

A plane-polarised light is incident perpendicularly on a quartz plate cut with faces parallel to optic axis. Find the thickness of the quartz plate which introduces phase difference of 60^\circ between e- and o-rays.

Show that the plane of polarisation is rotated through \theta = \frac{\delta}{2} = \frac{\pi d}{\lambda} (\mu_L - \mu_R) in optical rotation where symbols have their usual meanings.

What are the important properties of a hologram?

At what temperature are the rates of spontaneous and stimulated emission equal? (Assume \lambda = 500\text{ nm})

What are the characteristics of stimulated emission? Show that in the optical region, stimulated emission is negligible compared to spontaneous emission.

Optical power of 1\text{ mW} is launched into an optical fiber of length 100\text{ m}. If the power emerging from the other end is 0\cdot 3\text{ mW}, calculate the fiber attenuation.

For stationary waves on a string whose ends are fixed, show that the energy density is maximum at antinodes and minimum at nodes.

Derive the condition for achromatism of two thin lenses separated by a finite distance and made up of same material.

Let E_A = E_1 \sin \omega t \quad \text{and} \quad E_B = E_2 \sin (\omega t + \delta) By using analytical method, obtain an expression to explain interference. Also show that intensity varies along the screen in accordance with the law of cosine square in interference pattern.

Explain the phenomenon of interference in thin films. Why is the contrast better in brightness of fringes obtained from the interference of reflected light rays compared to the transmitted light rays?

Obtain an expression for the resolving power of a plane transmission grating. Deduce the missing orders for a double-slit Fraunhofer pattern, if the slit widths are 0\cdot 16\text{ mm} and 0\cdot 8\text{ mm} apart.

Show that a four-dimensional volume element dx\,dy\,dz\,dt is invariant to Lorentz transformation.

Obtain the relativistic equation for aberration of light using velocity transformation equations.