Define gauge transformation. Under what condition can the gauge transformation be regarded as restricted gauge transformation ? Further, generate the symmetrical forms of Maxwell's equations in terms of scalar and vector potentials under Lorentz gauge.
What are geomagnetic storms and why are they potentially disruptive to power grids ?
In the circuit as shown in figure :
where V = 10\text{ V}, R = 10\ \Omega, L = 1\text{ H}, C = 10\ \mu\text{F}, and v_c(0) = 0, find i(0+), \dfrac{di}{dt}(0+) and \dfrac{d^2i}{dt^2}(0+).
The impedance function of a parallel R, L and C circuit has poles loaded at - 3 \pm 4j\text{ radians/second}. If the value of \text{L} = 1\text{ Henry}, determine the following :
(i) The value of R and C.
(ii) What is the quality factor of this circuit ? Derive an expression for series and parallel circuit.
Show that in an A.C. circuit with inductor only, current lags behind emf in phase by \dfrac{\pi}{2}. If the current through 0\cdot 5\text{ Henry} inductor varies sinusoidally with an amplitude of 10\text{ amp} and a frequency 50\text{ Hz}, calculate the potential difference across the terminals of the inductor.
Write Maxwell's equations in differential and algebraic forms. Give the physical significance of each. Show that the equation of continuity is contained in Maxwell's equations.
In a step-index optical fiber system, explain the terms pulse dispersion and material dispersion. An optical fiber having refractive indices of core and cladding n_1 = 1.463 and n_2 = 1.444 respectively, uses a Laser diode with \lambda_0 = 1.50\,\mu\mathrm{m} with a spectral width of 2\,\mathrm{nm}. At this wavelength if the material dispersion coefficient, D_{m} is 18.23\,\mathrm{ps/(km\cdot nm)}, then calculate the pulse dispersion and material dispersion for 1\,\mathrm{km} length of the fiber.
What is damped harmonic oscillation? Write the equation of motion and obtain the general solution for this oscillation. Discuss the cases of dead beat, critical damping and oscillatory motion based on the general solution. What would be the logarithmic decrement of the damped vibrating system, if it has an initial amplitude 30\,\mathrm{cm}, which reduces to 3\,\mathrm{cm} after 20 complete oscillations?
A thin film of petrol of thickness 9 \times 10^{-6}\,\mathrm{cm} is viewed at an angle 30^\circ to the normal. Find the wavelength(s) of light in visible spectrum which can be viewed in the reflected light. The refractive index of the film \mu = 1.35.
Show that the phenomenon of Fraunhofer diffraction at two vertical slits is modulation of two terms viz. double slit interference and single slit diffraction. Obtain the condition for positions of maxima and minima.
A mass m is suspended by two springs having force constants k_1 and k_2 as shown in the figure. The mass m is displaced vertically downward and then released. If at any instant t, the displacement of the mass m is x, then show that the motion of the mass is simple harmonic motion having frequency f=\frac{1}{2\pi}\sqrt{\frac{1}{m}\left(\frac{k_1k_2}{k_1+k_2}\right)}
What is chromatic aberration? Obtain the condition for achromatism using combination of two thin lenses placed in contact to each other. Can this system work as achromatic doublet if both are of same material? Justify your answer.
What is the principle of propagation in optical fibers ? Explain with the help of neat diagram, the ray propagation in Step index and Parabolic index optical fibers. How can pulse dispersion be minimized using Parabolic index optical fibers ?
What is the Resolving power of a grating ? Obtain an expression for the Resolving power of a grating, based on Rayleigh's criterion of resolution.
Consider that a continuous laser beam which is assumed to be perfectly monochromatic with a wavelength of 6500\text{ \AA} is chopped into 2\text{ ns} pulses using a shutter. Calculate the number of photons in each pulse, if the power of each pulse is 5\text{ mW}.
What is holography ? Briefly discuss the applications of holography.
A body executes Simple Harmonic Motion such that its velocity at the mean position is 2\cdot 0\text{ m/s} and acceleration at one of the extremities is 1\cdot 57\text{ m/s}^2. Calculate the time period of vibration.
What are beats ? A tuning fork gives 6 beats per second with 25\cdot 4\text{ cm} length of stretched sonameter wire. The same 6 beats are heard per second when the length of the same wire is reduced to 24\cdot 6\text{ cm}. Calculate the frequency of the tuning fork.
What is achromatism ? Obtain the condition for achromatism of two thin lenses separated by a distance of x metres.
Two glasses have dispersive powers in the ratio 2 : 3. These glasses are used in the manufacture of an achromatic contact objective of focal length 50\text{ cm}. What are the focal lengths of the lenses ?
