UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Show that energy stored in a capacitor is \frac{1}{2} \frac{q^2}{C} while the energy stored in the inductor is \frac{1}{2} L i^2, where the symbols have their usual meaning.

Using Laplace's equation obtain an expression for the potential between two coaxial cylinders.

Obtain expressions for electrostatic scalar potential magnetostatic vector potential and electromagnetic potential. How are the first two related to the third? Explain the idea of retarded potential.

Show that it is possible to arrive at Stefan-Boltzmann law with the aid of Carnot's cycle using black body radiation as the working substance.

An excess charge placed on an insulated conductor, resides entirely on its outer surface. Priestly checked his observation and showed that the inverse square law of force followed from it. Explain.

A series circuit consisting of 410\text{ ohms} of resistance, 81.0\ \mu\text{H} of inductance and 225\ \mu\mu\text{F} of capacitance is excited by a constant voltage amplitude generator of variable frequency. At what frequency is the maximum power delivered?

What Poynting vector ? Explain how the transport of electromagnetic energy is expressed quantitatively by Poynting vector.

A harmonic emf is applied to a series circuit containing resistance, inductance and capacitance. Derive the expression for the current and condition for resonance.

Give the four basic experimental laws of electro magnetics in words and in mathematical form. Explain how they are modified to obtain the Maxwell's equations. Show how these equations lead to prediction about the speed at which e.m. waves are propagated in vacuum.

The total energy, U in oscillating L-C circuit is given by: U = U_B + U_E = \frac{1}{2} L i^2 + \frac{1}{2} \frac{q^2}{C} When the resistance of the circuit is zero From this show that it is an oscillatory circuit and find the time period.

If steady voltage is applied to an L-R circuit, show how voltage across the inductance and the current in the circuit changes with time. Explain the term inductive time constant.

State Biot-Savart's law. Derive an expression for the magnetic field at points along the axis of a circular coil.

State Planck's formula for black-body spectrum. Show that 'Planck's formula reduceds to Wien's formula at short wavelengths,

Show that the temperature (T) of a plant varies inversely as the square root of its distance (R) from the Sun. (The Sun and Planets are considered to be black-bodies in radiative equilibrium.)

In a nuclear explosion, the maximum temperature reached was of the order of 10^8\text{ K}. Estimate the order of wavelength at which the maximum of radiated energy occurs.

Write down Maxwell's equations for an isotropic homogenous dielectric and point out their relations with observational laws. How do the equations lead to the concept of electromagnetic waves?

Write a short note on Uniqueness theorem in electrostatics.

State Coulomb's law and show that the electric field can be derived from a potential function. If the charge distribution is continuous, find the integral formula for determining its field.

Two charges are placed at a distance of 1 metre. The magnitude of one charge is double that of the second charge. Find the neutral points in the two cases: (i) the charge are of the same sign (ii) the charge are of opposite sign. What happens to the neutral point if the two charges are of equal magnitude and opposite sign?

Write down Plank's law of radiation and establish Wien's law from it.