Show that the Amperes circuital law fails for time varying currents. How has this difficulty been overcome by Maxwell by introducing the concept of displacement current density? How is the expression for \vec{A} \times \vec{B} modified for magnetized material for magnetisation vector \vec{M} ?
What is the synchronization condition in a cyclotron? Under identical magnetic flux density, show that the kinetic energy of an accelerated \alpha-particle is equal to that of proton. What should be the frequencies of r.f. electric fields for \alpha-particles and proton, respectively placed under the same magnetic flux density?
An alternating voltage of varying frequency is applied across a two-branch parallel circuit of R_1 and L in series and R_2 and C in series as shown in Fig. below.
Find its resonant frequency. If R_1 and R_2 are not zero, state the conditions when the resonant frequency is given by f_0 = \frac{1}{2\pi \sqrt{LC}}
An alternating voltage is applied to CR circuit connected in series. Under what conditions it acts as an (i) integrator and (ii) a differentiator?
How does a ferromagnetic material get magnetized? Why is the demagnetization process irreversible? What is the physical significance of the magnetic hysteresis loop for a ferromagnetic material? Under what conditions the ferromagnetic materials become paramagnetic ?
The solar constant on the lighted surface of the earth is given as ‘J’ Assuming solar radiation as black body radiation find an expression for the temperature of the photosphere of the sun.
Obtain the intensity pattern due to Fraunhofer diffraction at two parallel slits. Each slit has a width ‘a’ and the separation between the slits is d. How many interference fringes will appear in the central diffraction maximum, it d = 4a?
A body of mass m supported by a spiral spring causes an extension of d is the spring. The body is set in vertical oscillations of small amplitude. Find an expression for the periodic time of the oscillations.
Show that for forced oscillations amplitude resonance and energy resonance do not occur at the same frequency.
Write a short note on Fourier transformation.
In a biprism experiment the fringe-width with lightly of wavelength \lambda = 5900\text{ \AA} is 0.43\text{ mm}. On introducing a mica sheet in the path of one of the interfering rays the central fringe shifts by 1.89\text{ mm}. If refractive index of mica is 1.59, calculate the thickness of the sheet.
A left circularly polarized beam of light (\lambda = 6000\text{ \AA}) is incident on a quartz crystal (Optic axis parallel to the surface). Find the state of polarisation of the emergent beam. (Thickness of quartz crystal = 2.3 \times 10^{-5}\text{ m}, \mu_e = 1.5538, \mu_o = 1.5444)
Discuss the working principle of He-Ne laser indicating the transitions involved in the process. Determine the power output of a laser in which a 3.0\text{ J} pulse is delivered in 1.0\text{ ns}.
The potential energy of a particle is given by U = a \cos \alpha x Obtain the positions of stable equilibrium.
What are precession an nutation ? Show that the angular velocity of precession \vec{\Omega} is related to the angular momentum \vec{L} and external torque \vec{r} as \vec{\Omega} \times \vec{L} = \vec{r} Assume \Omega \ll \omega.
State Kepler’s laws and prove that for elliptical orbits the square of the period of a satellite is proportional to the cube of the semi-major axis.
A satellite is launched into a circular orbit close to the surface of the earth. Fine an expression for the additional velocity that has to be imparted to the satellite to overcome the gravitational pull.
The distance between the centres of oxygen and carbon atoms in a carbon monoxide molecule is 1.2\text{ \AA}. Determine the position of the centre of mass of the molecule relative to carbon. (Assume atomic masses of carbon and oxygen as 12 and 16 respectively.)
Write a short note on Michelson - morley experiment.
In the relativistic region, compare the relative increase in velocity with the relative increase in energy of a particle.
