Show that the steady -state energy is stored in the magnetic field.

What is the limiting case of a metallic conductor in the above case ? Explain

Using Maxwell's equations, derive the electromagnetic wave equations for a conducting medium and solve it.

The introduction of the displacement current is one of the major contributions of Maxwell. Discuss.

Find the power dissipated by R and power stored in L.

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.

Two inductance coils hang inductances L_1 and L_2 and negligible resistances are connected in parallel. The coils have a mutual inductance M. Obtain an expression for the effective inductance of the combination.

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 ?

The electric field vector of a plane electromagnetic wave is given by: \vec{E} = E_0 \cos(kz - \omega t + \delta)\hat{x} Write the magnetic field vector. Calculate the average energy per unit volume stored in electromagnetic field and the average energy flux density.

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.

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.

Derive the wave equations for \vec{E} and \vec{B} and solve one of these for plane wave propagation in an unbounded, homogenous dielectric medium. Further show that in a plane wave (\vec{E}, \vec{B}, \vec{K}) form a mutually orthogonal right-handed system.

Write down the expression for the energy distribution for the black body radiations at temperature T. Show that this expression goes into the Rayleigh-Jeans distribution at one end of the frequency spectrum and the Wiens distribution at the other end.

A deuteron of kinetic energy 40 keV is describing a circular orbit of radius 0.6 m in a plane perpendicular to a magnetic induction \vec{B}. Calculate the kinetic energy of a proton that describes a circular trajectory of radius 0.8 m in the same plane with the same \vec{B}.

What was the basis for light to be accepted as an electromagnetic wave ? The \vec{E} vector in a light wave polarised in the (x, y) plane is expressed as \vec{E}(x, y, z, t) = \vec{E}_0 \sin\left[\omega t - k(x + y)\right] Determine the propagation and the polarisation vectors.

A travelling electromagnetic wave is described by the equation. E_x(z, t) = 0.5 \cos (20t - 2z) Determine: (i) Speed of the wave, v (ii) Wavelength. \lambda (iii) Time period, T (iv) Direction of propagation

A series LCR circuit has L = 20\text{ mH}, C = 0.5\ \mu\text{F} and R = 10\,\Omega. The circuit is driven by an alternating emf with amplitude 200\text{ V}. Calculate (i) resonance frequency (ii) the current at resonance frequency (iii) Q value and (iv) half width of the resonance current.

Two coils are connected in series and their total self inductance is 4.40 mH. When one coil is reversed, the total self-inductance is 1.60 mH. All the flux due to the first coil links the second coil, but only 40% of the flux due to the second coil links the first coil. Find the self-inductance of each of the coils and their mutual inductance.

A potential difference with a frequency of 50 cycles per second is applied to a coil of resistance 1 k ohms and inductance 2H. Calculate the power factor of the circuits.