Calculate the electric field as a function of position due to a dipole whose potential is given by V = \frac{P \cos \theta}{4 \pi \epsilon_0 r^2} \quad \text{where } r = \sqrt{x^2 + y^2} The dipole is located at the origin of the x, y axis system.
From Planck's radiation law, derive Wien's displacement law and Rayleigh Jean's law.
Derive the energy continuity equation for electromagnetic waves using the poynting vector.
Define scalar and vector potentials. Recast Maxwell's equations in terms of these potentials.
What is gauge transformation? Define coulomb gauge. Derive the equation for vector potential under coulomb gauge.
Show that the steady -state energy is stored in the magnetic field.
The introduction of the displacement current is one of the major contributions of Maxwell. Discuss.
Using Maxwell's equations, derive the electromagnetic wave equations for a conducting medium and solve it.
What is the limiting case of a metallic conductor in the above case ? Explain
Calculate the voltage drops across R and across L.
At what time are these voltage drops equal?
Find the power dissipated by R and power stored in L.
For an R-L- C series resonant circuit, show that f_0 = \sqrt{f_1 f_2}, where f_0 is the resonance frequency and f_1, and f_2 are the half-power frequencies. Is this relation true for a parallel resonance circuit in which R, L and C are connected in parallel to each other? Explain.
A series R-L circuit has a constant d.c. voltage V applied at the time t = 0 by closing a switch. Derive an expression for the current in the circuit.
Current is flowing in a single-turn circular coil of radius 0.1\text{ m} such that at a point 5\text{ mm} from the centre of the coil on the axis perpendicular to the plane of the coil the magnetic field is 0.1\text{ mT}. Find the current in the coil. Hence calculate the magnetic moment of the current carrying coil.
The frequency of applied voltage in a cyclotron is 1.2 \times 10^7\text{ Hz}. Find the magnetic field strength when protons are to be accelerated. If the radius of dees is 0.5 m, what is the energy of the accelerated protons ?
An L–C–R circuit has a resistance of 100 ohms, a capacitance of 0.2 \mu\text{F} and an inductance of 5 H. An ac source E = 50 \sin (1000 t)\text{ volt} is connected in the circuit. Calculate the average power dissipated.
In the given circuit the output voltage v_0 at time t second after closing the key K is 1 volt. Calculate the rate of change of current in the inductance coil at this moment.
In a series L–C–R circuit connected to an alternating constant voltage source the current amplitude is (1/n) times the amplitude at resonance at frequencies w_1 and w_2. Obtain an expression for its quality factor at resonant frequency.
A potential field is given by: \phi = (x^2 + y^2 + z^2)\text{ volt.} Find the electric field at a point (x, y, z) and the charge density in the region.
