Search, filter, and study UPSC Civil Services & IFoS Physics past year questions with rigorous derivations, formulas, and step-by-step solutions.
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.
Using the set of four Maxwell's equations, obtain the Lorentz condition relation between the scalar potential \phi and vector potential A, i.e., \nabla \cdot A + \frac{1}{c^2} \frac{\partial \phi}{\partial t} = 0 and discuss the gauge transformations, Lorentz gauge and Coulomb gauge.
There is a potential gradient of 100\text{ V/m} normal to the surface of the earth. Assuming the earth to be a charged sphere of radius 6370\text{ km}, find the total charge on the earth.
(i) Show that the electric and magnetic energy densities in a plane travelling wave are equal. Also prove that the total energy density = \varepsilon_0 E^2 = \mu_0 H^2.
(ii) Deduce the equation of continuity based on Maxwell's 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}.
Obtain an expression for the electric potential and electric field strength at a point due to an electric dipole.
(i) The equation for an alternating current is I = 42\cdot 42 \sin (314t). Find the following : Maximum value of current, Frequency, RMS value and Average value
(ii) A condenser of capacity 1~\mu\text{F} is first charged and then discharged through a resistance of 1\text{ M}\Omega. Calculate the time in which the charge on the condenser will fall to 50\% of its initial value.
(iii) Consider the displacement vector \vec{D}, given by \vec{D} = (10xyz^2 + 4x)\hat{i} + (5x^2 z^2)\hat{j} + (10x^2 yz)\hat{k}\text{ nC/m}^2 Find the total charge enclosed in a cube of volume 10^{-9}\text{ m}^3 located at the point (1, 2, 3).
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.
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.
Construct the Hamiltonian of a charged particle with charge q and mass m moving with the velocity \vec{v} in the external electromagnetic field, \vec{E}=E_0 \hat{i}, \vec{B}=B_0 \hat{k}, where E_0 and B_0 are constants.
In free space, the electric field of electromagnetic wave is given by \vec{E}(x, t) = 100 \cos (\omega t - kx) \hat{y}\text{ volt/metre} Find the average power crossing a circular area of radius 2\text{ metres} in the yz-plane.
(i) How are linearly polarised and circularly polarised lights generated from unpolarised light and are analysed?
(ii) A calcite crystal is to be used for producing a quarter wave plate. The refractive indices of the crystal for ordinary ray and extraordinary ray are 1\cdot 65836 and 1\cdot 48641 respectively. What is the thickness of the plate required if the light of wavelength 632\cdot 8\text{ nm} is to be used?
(i) What is population inversion? How is it efficiently achieved in He-Ne laser? Show it with necessary energy levels diagram.
(ii) Show that for a normal optical source emitting at 600\text{ nm} at a temperature of 10^3\text{ K}, the spontaneous emission dominates over stimulated emission.
Distinguish between positive and negative crystals in terms of double refraction. How are these crystals used to make quarter wave plates? Explain how the quarter wave plate is used in producing elliptically and circularly polarized light.
Explain the principle and working of He-Ne laser. What is the role of He gas? Why is it necessary to use narrow tube? How many longitudinal modes can be excited for an He-Ne laser in a cavity of length 30 cm and having half width of gain profile of laser material 2 \times 10^{-3}\,\mathrm{nm}? The emission wavelength is 6328\,\mathring{\mathrm{A}}.
(i) When a monochromatic light passes through a single slit, dark and bright fringes are observed on a screen kept far away from the slit. Draw an amplitude and intensity pattern of the light on the screen.
(ii) Write an expression for intensity distribution and give the conditions for bright and dark fringes.
(iii) If the slit width is 0\cdot 3\text{ mm} and the distance between the screen and the slit is about 30\text{ cm}, then what is the angle of diffraction for the first minimum? (\lambda = 5 \times 10^{-5}\text{ cm})
A plane transmission grating has 3000 lines in all, having width of 3\ \mathrm{mm}. What would be the angular separation in the first order spectrum of the two sodium lines of wavelengths 5890\mathring{\mathrm{A}} and 5896\mathring{\mathrm{A}}? Can they be seen distinctly?
Discuss the intensity distribution in Fraunhofer diffraction pattern due to a single slit. Obtain conditions for maxima and minima of the intensity distribution. Show that the intensity of the first maxima is about 4.95\% of that of the principal maxima.
Thin transparent films produce colours when a white light falls on them or they act as antireflecting coatings. Find the conditions for these characteristics.
With the help of a neat diagram, explain spherical aberration. Briefly discuss the methods to minimize spherical aberration.