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?
An electric dipole is placed in an external electric field. Find the interaction energy between the electric dipole and the field. And hence find the force and the torque acting on the dipole.
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 expressions for electrostatic scalar potential magnetostatic vector potential and electromagnetic potential. How are the first two related to the third? Explain the idea of retarded potential.
State and prove Poynting's theorem. Discuss the physical significance of each term in resulting equation.
Show that the electromagnetic waves in free space are transverse in nature.
If the avenge distance between the sun and earth is 1.5 \times 10^{11} m, find the avenge solar energy flux and the earth (solar constant) given the power radiated by the sun = 3.8 \times 10^{26} watt.
Calculate \omega_0 \Delta \omega and quality factor Q for LCR parallel resonant circuit given the values C = 0.4 \muF, L = 4 mH and R = 1 K\Omega.
A harmonic e.m.f. is applied to a parallel resonant circuit containing resistance R, inductance L and capacitance C. Derive expressions for resonance, angular frequency \omega_0 and the band width \Delta \omega.
Show that energy stored in a capacitor is \frac{1}{2} \frac{q^2}{C} while the energy stored in the inductor is \frac{1}{2} L i^2, where the symbols have their usual meaning.
Using Laplace's equation obtain an expression for the potential between two coaxial cylinders.
Show that it is possible to arrive at Stefan-Boltzmann law with the aid of Carnot's cycle using black body radiation as the working substance.
An excess charge placed on an insulated conductor, resides entirely on its outer surface. Priestly checked his observation and showed that the inverse square law of force followed from it. Explain.
Give the four basic experimental laws of electro magnetics in words and in mathematical form. Explain how they are modified to obtain the Maxwell's equations. Show how these equations lead to prediction about the speed at which e.m. waves are propagated in vacuum.
What Poynting vector ? Explain how the transport of electromagnetic energy is expressed quantitatively by Poynting vector.
A harmonic emf is applied to a series circuit containing resistance, inductance and capacitance. Derive the expression for the current and condition for resonance.
A series circuit consisting of 410\text{ ohms} of resistance, 81.0\ \mu\text{H} of inductance and 225\ \mu\mu\text{F} of capacitance is excited by a constant voltage amplitude generator of variable frequency. At what frequency is the maximum power delivered?
If steady voltage is applied to an L-R circuit, show how voltage across the inductance and the current in the circuit changes with time. Explain the term inductive time constant.
