UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Derive an expression for the thermal efficiency of a reversible heat engine operating on the Diesel cycle with an ideal gas of constant heat capacity as the working medium.

Calculate the number of different arrangements of 10 indistinguishable particles in 15 cells of equal a priori probability, considering that one cell contains only one particle.

Consider the following statement: ``The Fermi energy of a given material is the energy of that quantum state which has the probability equal to \frac{1}{2} of being occupied by the conduction electrons.'' Is the above statement correct? Give reasons for your answer.

Explain the term 'Poynting vector' and state the significance of Poynting theorem.

Calculate the skin depth for radio waves in free space of wavelength 3 m in copper, given that electrical conductivity for copper is 6\times10^{7}\,\Omega^{-1}\,\mathrm{m}^{-1}.

Discuss the growth of current when an e.m.f. is suddenly applied to a circuit containing resistance, inductance and capacitance in series. What is the time constant of the circuit?

A series circuit has an inductance of 200 microhenries, a capacitance of 0.0005 microfarad and a resistance of 10 ohms. Find the resonant frequency and quality factor of the circuit.

What happens if the primary winding of a transformer is connected to a battery?

Calculate, giving necessary steps, the radio frequency at which nuclear magnetic resonance occurs in water kept in a uniform magnetic field of 2.4\ \mathrm{T}. The magnetic moment of proton is 2.793\mu_N.

Obtain Poisson's equation in electrostatics from Gauss' law. What form does it take when the charge density is zero?

What is meant by a dielectric? Define polarization vector P and relate it with the average molecular dipole moment. Obtain expression for the potential due to a polarized dielectric in terms of the polarization vector.

A wire of length 2 m is perpendicular to X-Y plane. It is moved with a velocity \vec{V}=(2\hat{i}+3\hat{j}+\hat{k})\,\mathrm{ms}^{-1} through a region of uniform induction \vec{B}=(\hat{i}+2\hat{j})\mathrm{Wm}^{-2}. Compute the potential difference between the ends of the wire.

Using Maxwell's field equations for a homogeneous non-conducting medium, derive the wave equation for the electric field. Calculate the velocity of EM wave in free space.

A laser beam of 1 micrometer wavelength with 3 megawatts power of beam diameter 10\ \mathrm{mm} is focussed by a lens of focal length 50\ \mathrm{mm}. Evaluate the electric field associated with the light beam at the focal point. (Dielectric permittivity of free space, \varepsilon_0=8\cdot8542\times10^{-12}\ \mathrm{C^2/N-m^2})

Obtain the expression for the primary focal length of Fresnel zone plate.

An unpolarized light beam of intensity 1000\ \mathrm{W/m^2} is incident on an ideal linear polarizer with its transmission axis parallel to vertical direction. Describe an experiment to reduce the intensity of light beam to 500\ \mathrm{W/m^2}.

Show that two light beams polarized in perpendicular directions will not interfere.

What should be the refractive index of cladding of an optical fibre with numerical aperture 0.5 with refractive index of core as 1.5?

Describe Michelson interferometer for evaluation of coherence length of an optical beam. Calculate coherence length of a light beam of wavelength 600\,\mathrm{nm} with spectral width of 0.01\,\mathrm{nm}.

In the propagation of longitudinal waves in a fluid contained in an infinitely long tube of cross-section A, show that \rho=\rho_0\left(1-\frac{\partial\xi}{\partial x}\right) where, \rho_0 = equilibrium density \rho = density of the fluid in the disturbed state \frac{\partial\xi}{\partial x}=\text{volume strain}\quad\left(\left|\frac{\partial\xi}{\partial x}\right|\ll1\right)