UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Show that the steady -state energy is stored in the magnetic field.

Current is flowing in a single-turn circular coil of radius 0.1\text{ m} such that at a point 5\text{ mm} from the centre of the coil on the axis perpendicular to the plane of the coil the magnetic field is 0.1\text{ mT}. Find the current in the coil. Hence calculate the magnetic moment of the current carrying coil.

A series R-L circuit has a constant d.c. voltage V applied at the time t = 0 by closing a switch. Derive an expression for the current in the circuit.

For an R-L- C series resonant circuit, show that f_0 = \sqrt{f_1 f_2}, where f_0 is the resonance frequency and f_1, and f_2 are the half-power frequencies. Is this relation true for a parallel resonance circuit in which R, L and C are connected in parallel to each other? Explain.

Find the power dissipated by R and power stored in L.

A potential field is given by: \phi = (x^2 + y^2 + z^2)\text{ volt.} Find the electric field at a point (x, y, z) and the charge density in the region.

In the given circuit the output voltage v_0 at time t second after closing the key K is 1 volt. Calculate the rate of change of current in the inductance coil at this moment.

An L–C–R circuit has a resistance of 100 ohms, a capacitance of 0.2 \mu\text{F} and an inductance of 5 H. An ac source E = 50 \sin (1000 t)\text{ volt} is connected in the circuit. Calculate the average power dissipated.

The frequency of applied voltage in a cyclotron is 1.2 \times 10^7\text{ Hz}. Find the magnetic field strength when protons are to be accelerated. If the radius of dees is 0.5 m, what is the energy of the accelerated protons ?

Two inductance coils hang inductances L_1 and L_2 and negligible resistances are connected in parallel. The coils have a mutual inductance M. Obtain an expression for the effective inductance of the combination.

The electric field vector of a plane electromagnetic wave is given by: \vec{E} = E_0 \cos(kz - \omega t + \delta)\hat{x} Write the magnetic field vector. Calculate the average energy per unit volume stored in electromagnetic field and the average energy flux density.

In a series L–C–R circuit connected to an alternating constant voltage source the current amplitude is (1/n) times the amplitude at resonance at frequencies w_1 and w_2. Obtain an expression for its quality factor at resonant frequency.

A series LCR circuit has L = 20\text{ mH}, C = 0.5\ \mu\text{F} and R = 10\,\Omega. The circuit is driven by an alternating emf with amplitude 200\text{ V}. Calculate (i) resonance frequency (ii) the current at resonance frequency (iii) Q value and (iv) half width of the resonance current.

Derive the wave equations for \vec{E} and \vec{B} and solve one of these for plane wave propagation in an unbounded, homogenous dielectric medium. Further show that in a plane wave (\vec{E}, \vec{B}, \vec{K}) form a mutually orthogonal right-handed system.

A travelling electromagnetic wave is described by the equation. E_x(z, t) = 0.5 \cos (20t - 2z) Determine: (i) Speed of the wave, v (ii) Wavelength. \lambda (iii) Time period, T (iv) Direction of propagation

Two coils are connected in series and their total self inductance is 4.40 mH. When one coil is reversed, the total self-inductance is 1.60 mH. All the flux due to the first coil links the second coil, but only 40% of the flux due to the second coil links the first coil. Find the self-inductance of each of the coils and their mutual inductance.

A potential difference with a frequency of 50 cycles per second is applied to a coil of resistance 1 k ohms and inductance 2H. Calculate the power factor of the circuits.

Define quality factor for an A.C. circular and discuss the meaning of electrical resonance in a series LCR circuit. Explain the term sharpness of resonance.

Determine the energy of attraction between an electric dipole and a plane conducting surface at zero potential.

A deuteron of kinetic energy 40 keV is describing a circular orbit of radius 0.6 m in a plane perpendicular to a magnetic induction \vec{B}. Calculate the kinetic energy of a proton that describes a circular trajectory of radius 0.8 m in the same plane with the same \vec{B}.