Search, filter, and study UPSC Civil Services & IFoS Physics past year questions with rigorous derivations, formulas, and step-by-step solutions.
The four arms of a Wheatstone bridge have the following resistances: AB = 100\,\Omega, BC = 10\,\Omega, CD = 5\,\Omega, DA = 60\,\Omega A galvanometer of 15\,\Omega resistance is connected across BD. Calculate the current through the galvanometer when a potential difference of 10 volts is maintained across AC.
Prove that the Maxwell's equations in a medium contain the conservation of charge in differential form.
Justify which of the four Maxwell's equations imply that there are no magnetic monopoles. How these equations would have been written if they were?
The electric field in a medium is given by \vec{E} = \vec{E}_0 e^{-\alpha z} \sin(kz - \omega t), where \vec{E}_0 is a constant vector with dimensions of the electric field. Prove that \vec{E} cannot have a component along the unit vector, \hat{z}, parallel to the z-axis. Here \alpha is a positive constant.
The plane y = 5 carries a current of density 10\\ \hat{z} \text{ (Amp/m)}. Calculate the value of the magnetic field \vec{H} at the point (0, 1, -5).
The current density in spherical co-ordinates is given by \vec{J} = \frac{1}{r^3} \left[ 2 \cos \theta \hat{r} + \sin \theta \hat{\theta} \right] \text{A/m}^2 where \hat{r} and \hat{\theta} are unit vectors. Calculate the amount of current passing through a hemisphere of radius 20\text{ cm}.
Consider Maxwell's equation in differential form in media. For j=\rho=0, assume \epsilon=\epsilon_0e^{\alpha t} and \mu=\mu_0e^{\alpha t} and show that the relevant wave equation for a plane wave propagating along x-direction is \frac{\partial^2 E}{\partial x^2}=\mu\frac{\partial^2 D}{\partial t^2}+\mu\alpha\frac{\partial D}{\partial t} where \vec{E}=E\hat{y} and \vec{H}=H\hat{z}.
A resistor R(= 6.2\,\mathrm{M}\Omega) and a capacitor C(= 2.4\,\mu\mathrm{F}) are connected in series and a 12 V battery of negligible internal resistance is connected across their combination.
(i) What is the capacitive time constant of this circuit?
(ii) At what time, after the battery is connected, does the potential difference across the capacitor become 5.6 V?
Consider an infinite line charge with charge density \rho\text{ coulomb/meter} located at a distance d\text{ meters} from a grounded conducting plane z = 0. Determine : (i) the magnitude of the potential V for z > 0 and z \le 0. (ii) the surface charge density induced on the conducting plane.
Consider an infinite current sheet with a uniform current density \vec{K} \text{ (Amp/m)}. Show that the magnetic field \vec{H} at a point away from the sheet is \vec{H} = \frac{1}{2} \vec{K} \times \hat{n} where \hat{n} is a unit normal vector directed from the current sheet to the point.
Find out the total electric potential energy of a single spherical object of uniform charge density \rho, total charge Q and radius R.
Consider a plane wave travelling along the positive y-direction incident upon a glass of refractive index n=1.6. Find the transmission coefficient.
Determine the torque experienced by an electric dipole of moment \vec{p} if placed in an electric field \vec{E} in nonaligned state. Also show that the interaction energy of two dipoles of moments \vec{p}_1 and \vec{p}_2 separated by a displacement \vec{r} is U=\frac{1}{4\pi\epsilon_0}\frac{1}{r^3}\left[\vec{p}_1\cdot\vec{p}_2-3(\vec{p}_1\cdot\hat{r})(\vec{p}_2\cdot\hat{r})\right] assuming the expression for field due to a dipole.
If the magnetic field \vec{B}, at a point with position vector \vec{r} is uniform, show that the corresponding vector potential \vec{A}(\vec{r}) is given by \vec{A}(\vec{r}) = -\frac{1}{2} \left[ \vec{r} \times \vec{B} \right].
An inductor of inductance 5\text{ H} is suddenly connected to a 10\text{ V} d.c. power supply through a resistor of 10\\ \Omega. After what time will the current in the circuit be 1/10\text{th} of its steady state value ?
When a thin film of a transparent material is put behind one of the slits in Young's double-slit interference experiment, the zero-order fringe moves to the position previously occupied by the fourth-order bright fringe. The index of refraction of the film is n=1.2 and the wavelength of light, \lambda=5000\,\mathring{\mathrm{A}}. Determine the thickness of the film.
For calcite, the refractive indices of ordinary and extraordinary rays are 1.65836 and 1.48641 at \lambda_0=5893\,\mathring{\mathrm{A}} respectively. A left circularly polarized beam of this wavelength is incident normally on such crystal of thickness 0.005141\,\mathrm{mm} having its optic axis cut parallel to the surface. What will be the state of polarization of the emergent beam?
A light spring of relaxed length 'a_0' is suspended from a point. It carries a mass 'm' at its lower free end, which stretches it through a distance l. Show that the vertical oscillation of the system is simple harmonic in nature and has time period T = 2\pi \sqrt{l / g}, where g is the acceleration due to gravity.
Prove that the group velocity V_g of electromagnetic waves in a dispersive medium with refractive index n(\lambda_0) at wavelength \lambda_0 is given by V_g=\frac{c}{n(\lambda_0)-\lambda_0\dfrac{dn(\lambda_0)}{d\lambda_0}} where c is the free space velocity of light. Find the time taken for the electromagnetic pulse to travel a distance D.
Bring out the essential differences between the physical principles of spontaneous and stimulated emission of radiation. Why is it difficult to get efficient lasing action in case of an ideal two-level material system? Can you propose a scheme to enhance efficiency? Discuss.