UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Starting from Biot Savart's law, find the vector potential at a distance r, from a current carrying wire.

Show that attenuation constant \alpha and phase factor \beta for an electromagnetic wave, propagating in a perfectly conducting medium, are equal. At what frequency the skin depth in silver is 1\ \mu\text{m} when the conductivity of silver is 30 \times 10^6\text{ Siemens/meter} and relative permeability is 1.0?

Show that electromagnetic propagating in a homogeneous isotropic medium, arc transverse in nature.

An alternating voltage is applied to the circuit shown in Fig. 1. Show that it has two resonant frequencies, f_p and f_s interrelated as f_p = f_s \sqrt{\left(1 + \frac{1}{r}\right)} Where r = \left(\frac{C_b}{C_a}\right)

An electric dipole moment, \vec{p}_2, is placed at (r, \theta) in he electric field of another dipole moment \vec{p}_1, placed at he origin. Assuming that the electric potential, V, at (r, \theta) due to \vec{p}_1 is V(r, \theta) = \frac{p_1 \cos \theta}{4 \pi \epsilon_0 r^2} find the dipole-dipole interaction energy.

Self inductance of two coils, A and B, connected in series is 25\text{ mH} or 10\text{ mH}, depending on the relative current directions in the coils. Self inductance of the isolated coil. A, is 10\text{ mH}. Calculate mutual inductance M of the pair of coils coupling factor and leakage factor. If the current in coils is changing at the rate of 1000\text{ A/s}, find the induced electromotive forces across the coil A.

A relay has a coil resistance of 10\ \Omega and inductance of 1\text{ H}. It is energized by a single voltage pulse of 10\text{ V} which remains constant for 250\text{ ms} and then falls to 0\text{ V}. Relay contact closes when the increasing current reaches 200\text{ mA} and opens when the decreasing current is at 100\text{ mA}. Calculate the time for which the relay contact is closed.

How does a ferromagnetic material get magnetized? Why is the demagnetization process irreversible? What is the physical significance of the magnetic hysteresis loop for a ferromagnetic material? Under what conditions the ferromagnetic materials become paramagnetic ?

Starting from Maxwell equations obtain differential equations for scalar and vector potentials. Choosing the required gauge obtain identical differential equations for scalar and vector potentials. Solve the equation for scalar potential in a dielectric medium having a source of charge density p.

Show that the Amperes circuital law fails for time varying currents. How has this difficulty been overcome by Maxwell by introducing the concept of displacement current density? How is the expression for \vec{A} \times \vec{B} modified for magnetized material for magnetisation vector \vec{M} ?

What is the synchronization condition in a cyclotron? Under identical magnetic flux density, show that the kinetic energy of an accelerated \alpha-particle is equal to that of proton. What should be the frequencies of r.f. electric fields for \alpha-particles and proton, respectively placed under the same magnetic flux density?

An alternating voltage of varying frequency is applied across a two-branch parallel circuit of R_1 and L in series and R_2 and C in series as shown in Fig. below.

Find its resonant frequency. If R_1 and R_2 are not zero, state the conditions when the resonant frequency is given by f_0 = \frac{1}{2\pi \sqrt{LC}}

An alternating voltage is applied to CR circuit connected in series. Under what conditions it acts as an (i) integrator and (ii) a differentiator?

An electric dipole is placed in an external electric field. Find the interaction energy between the electric dipole and the field. And hence find the force and the torque acting on the dipole.

The solar constant on the lighted surface of the earth is given as ‘J’ Assuming solar radiation as black body radiation find an expression for the temperature of the photosphere of the sun.

State and prove Poynting's theorem. Discuss the physical significance of each term in resulting equation.

Show that the electromagnetic waves in free space are transverse in nature.

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.

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.

A harmonic e.m.f. is applied to a parallel resonant circuit containing resistance R, inductance L and capacitance C. Derive expressions for resonance, angular frequency \omega_0 and the band width \Delta \omega.