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.
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.
Determine the energy of attraction between an electric dipole and a plane conducting surface at zero potential.
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 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.
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}.
Define quality factor for an A.C. circular and discuss the meaning of electrical resonance in a series LCR circuit. Explain the term sharpness of resonance.
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.
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 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
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.
Obtain the characteristic impedance of the vacuum. Derive the expression used.
Write down Maxwell's equations in free space and hence show that the phase velocity of the electromagnetic wave is equal to the velocity of light in free space.
Calculate the magnetic moment of a coil having 100 turns, each of area 10\text{ cm}^2 carrying a current of 1\text{ mA}, flowing for 1\text{ ms}. The coil is placed in a magnetic field of 0.5\text{ kg} which is perpendicular to the magnetic moment. Calculate the torque acting on the coil and the angular momentum transferred to it.
Using Gauss law find the electric field inside a cylindrical capacitor and hence derive the expression for its capacitance. Find the dielectric constant of the material inside a 50\text{ mm} long capacitor of capacitance 40\ \mu\text{F} having inner conductor of radius 1\text{ mm}, outer conductor of radius 10\text{ mm}. Which of the materials has such a value of the dielectric constant ?
The self inductance of primary and secondary coils of a R.F. transformer is 10\text{ mH} each. When the coils are connected in series self resonating frequencies are 132.6\text{ kHz} and 108.3\text{ kHz}. Calculate the mutual inductance between the coils and the winding capacitance.
An alternating voltage, v = V_0 \sin (\omega t + \phi) is applied to a series RL circuit through a switch. Find the sum total of the transient and steady currents. Find the conditions when transient current becomes
(i) zero, and
(ii) maximum
Derive the distribution law which explains the black body spectrum over the entire wavelength region. Using this relation determine the value of Wiens constant b.
Write a short note on Solar constant.
