UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Based on the hysteresis loops for soft iron and steel as shown in the diagram, which material would you prefer to utilise for making transformer cores and why?

Write expressions for divergence and curl of an electrostatic field. From these, obtain Poisson and Laplace equations. Two concentric conducting spherical shells having radii r_1 and r_2 (r_1<r_2) are charged to potentials V_1 and V_2, respectively. What are the electric potential and hence electric field in the space between the shells? Also find the charge on the inner shell.

A vertically oriented electric dipole having dipole moment \vec{p} is kept at height h above an infinitely large horizontal conducting plate, which is grounded as shown in the diagram. Calculate the force between the electric dipole and the conducting plate by using method of images.

In a certain cyclotron, the maximum radius that the path of a deuteron may have before it is deflected out of the magnetic field is 20\,\mathrm{cm}.

(i) Calculate the velocity of the deuteron at this radius.

(ii) What is the energy of deuteron in \mathrm{MeV}? Given, magnetic field =1500 gauss and mass of deuteron =3.34\times10^{-27}\,\mathrm{kg}.

Three cells are connected in parallel with similar poles connected together with wires having negligible resistance. The emfs of the cells are 2, 1 and 4 volts respectively and the corresponding internal resistances are 4, 3 and 2 ohms. Calculate the current flowing through the 4 V cell.

Find the values of \mathrm{E} and \mathrm{H} on the surface of a wire carrying a current. By computing the Poynting vector, show that it represents a flow of energy into the wire.

Discuss in brief the ultraviolet catastrophe. How did Planck solve this problem?

Why do we prefer to work with a critically damped ballistic galvanometer in a laboratory? What is external critical damping resistance?

Two conducting planes, intersecting at right-angles to each other, are kept at a potential \phi_0. Calculate the potential at a point in space if the total charge on a plane of area \alpha be Q.

Briefly outline the theory of scattering of electromagnetic radiation by a bound electron and hence derive the conditions for Rayleigh scattering. How can you explain the blue of the sky?

Starting from the expression for the electrostatic potential \phi(\vec{r})=\frac{1}{4\pi\varepsilon_0}\int_V\frac{\rho(\vec{r}_0)}{|\vec{r}-\vec{r}_0|}\,dV_0 obtain Poisson's equation \nabla^2\phi=-\frac{\rho}{\varepsilon_0}. [Symbols have their usual meanings]

Find the capacitance of two concentric spherical metal shells having radii a and b.

Two solenoids have 500 and 800 turns of wire and are placed co-axially close to each other. A current of 5.0 A in the first solenoid produces an average flux of 200\mu\mathrm{Wb} through its each turn and a flux of 100\mu\mathrm{Wb} through each turn of the second solenoid. Find the self-inductance of the first solenoid and the mutual inductance of the solenoids.

Define a plane electromagnetic wave. A plane polarized wave is incident on the interface between two dielectric media. Obtain expressions for the amplitudes of the reflected and transmitted waves when the incident wave is polarized with its electric field B vector perpendicular to the plane of incidence. Discuss the phase relationships of the reflected and transmitted waves with respect to the incident wave.

A 12.0 V battery is connected at t=0 to a series combination of a resistor R=10.0\Omega and an inductor L=5.0\mathrm{H}. At what rate is energy being stored in the inductor when the current in the circuit is 0.4 A?

Write down Maxwell's equations in integral form. Explain the significance of each of these equations.

A 0.5\,\mathrm{m} long cylindrical medium between two conducting plates has uniform charge density of 100\,\mathrm{nC/m^3}. The axis of the cylindrical medium is along z-axis. The left plate is at z=0 and has a potential of 10\,\mathrm{kV} and the right plate is grounded. Determine the electric field at axial distance z=0.2\,\mathrm{m}.

A uniformly magnetized sphere of radius R has magnetization \vec{M}=M_0\hat{z}. If the scalar magnetic potentials inside and outside the sphere are given as under \phi_m=\frac{M_0}{3}z;\ r\leq R and \phi_m=\frac{M_0R^3}{3r^2}\cos\theta;\ r>R where, r,\theta are two spherical coordinates, find the magnetic field inside and outside the sphere.

A parallel plate capacitor has plate area =4.0\ \mathrm{cm^2} and plate separation =2.0\ \mathrm{mm}. An a.c. voltage V=20\sin(5\times10^{3}t) volts is applied across the plates. If the dielectric constant of the medium between the plates is \varepsilon_r=2.0, calculate the displacement current.

A current carrying circular wire loop of radius 1.0 cm has a magnetic moment 2.0\,\mathrm{mJ/T}. Determine the magnetic field at an axial distance of 3.0 cm from the centre of the loop.