Search, filter, and study UPSC Civil Services & IFoS Physics past year questions with rigorous derivations, formulas, and step-by-step solutions.
(i) Define Joule-Kelvin coefficient. Write it in its mathematical form. (ii) Determine the Joule-Kelvin coefficient for a van der Waals gas. Hence, obtain an expression for temperature of inversion. Discuss the conditions under which heating or cooling is produced.
A neutral atom consists of a point nucleus +q surrounded by a uniformly charged spherical cloud (-q) of radius r. Show that when such an atom is placed in a weak external electric field \vec{E}, the atomic polarizability of the atom is proportional to the volume of the sphere.
Find the energy stored in a system of four charges Q_1 = 1\text{ nC}, Q_2 = 2\text{ nC}, Q_3 = 3\text{ nC} and Q_4 = 4\text{ nC} placed at the cartesian coordinates R_1(1, 1), R_2(2, 1), R_3(1, 4) and R_4(2, 2), respectively. Assume free space.
Derive the expression for the inductance per unit length of two long parallel wires each of radius a, separated by distance d from their axes and carrying equal and opposite current I.
A circular ring of radius R lying on the x-y plane and centred at the origin, carries a uniform line charge \lambda. Find the first three terms (monopole, dipole and quadrupole) of the multipole expansion of potential V(r, \theta).
Two inductors having inductances L_1 and L_2 are connected in parallel. The inductors have a mutual inductance M. Derive the expression for the effective inductance. Assume the inductors have negligible resistances.
Show that Continuity equation is embedded in Maxwell's equations.
Write down the electromagnetic wave equation in non-conducting dielectric medium. Hence, show that the velocity of wave propagation is given by v = \sqrt{\frac{1}{\mu \epsilon}}, where the symbols have their usual meanings.
A spherical shell of radius R, carrying a uniform surface charge \sigma, is set spinning at angular velocity \omega about its axis. Find the vector potential it produces at point \vec{r}.
A material has \sigma = 10^{-2}\text{ S/m} and \varepsilon = 2\varepsilon_0. At what frequency, the conduction current would be equal to the displacement current?
An infinitely long coaxial cylinder structure has an inner conductor of radius a and an outer conductor of radius b. The inner conductor is attached to V_0, while the outer one is grounded. Calculate the field \vec{E} in between a and b.
If the electrostatic potential in spherical polar coordinate is \phi(r) = \phi_0 e^{-r/r_0} where \phi_0 and r_0 are constants, what will be the charge density at a distance r = r_0?
Explain Ampere's circuital law of magnetic field. What modifications Maxwell made in this equation to derive Maxwell's fourth equation?
The wire AB shown in the figure below has mass m, resistance r and it can slide on the smooth horizontal parallel rails separated by a distance l. A uniform magnetic field B exists in the rectangular region and a resistance R connects the rails outside the field region. At t = 0, the wire AB is pushed towards right with a speed v_0.
Find out the current in the loop at an instant when the speed of the wire is v. Find out the velocity v as a function of x. (Assume that the resistance of the rails is negligible)
Assuming that the Sun radiates like a perfect blackbody, at what wavelength does the peak of the solar spectrum occur? Given that the surface temperature of the Sun is about 6000\text{ K}.
Write down Stefan-Boltzmann law of radiation and derive it from Planck's law of radiation.
Two charges Q_1 = 3\text{ nC} and Q_2 = 4\text{ nC} are placed at the cartesian points (0, 2, 2)\text{ m} and (0, -2, 4)\text{ m}, respectively. The z = 0 plane is connected to the ground. Calculate the electric potential and the electric field at the point (3, 2, 4)\text{ m} using the method of images.
What is Lenz's law? Is Lenz's law the same as Faraday's law? What happens if Lenz's law is reversed? Explain.
Explain with proper examples the techniques of obtaining interference by 'division of wavefront' and 'division of amplitude'.
Find an expression for the average energy of a forced oscillator in the steady-state motion.