Pointing theorem; Vector and scalar potentials; Electromagnetic field tensor, covariance of Maxwell’s equations; Wave equations in isotropic dielectrics, Questions: Q 1. A region 1, z<0z<0z<0, has a dielectric material with ϵr=3.2\epsilon_r=3.2ϵr​=3.2 and a region 2, z>0z>0z>0 has a dielectric material with ϵr=2.0\epsilon_r=2.0ϵr​=2.0. Let the displacement vector in the region 1 be, D⃗1=−30ax+50ay+70aznCm−2\vec D_1 = -30a_x+50a_y+70a_z […]

Displacement current and Maxwell’s equations; Wave equations in vacuum, Questions: Q 1. For the electric field given by E=EoeiωtE= E_oe^{i\omega t}E=Eo​eiωt, show that the conduction current is in phase with the electric field, while the displacement currents lead the electric field by π/2\pi/2π/2 radians. Also, show that the displacement current in a good conductor is

Mean and r m s values in AC circuits; DC and AC circuits with R, L and C components; Series and parallel resonances; Quality factor; Principle of transformer. Questions: Q 1. A 10Ω10 \Omega10Ω resistor is connected in series with a capacitor of 1μF1 \mu F1μF and a battery with emf 12V12V12V. Before the switch

Magnetic shell, uniformly magnetized sphere; Ferromagnetic materials, hysteresis, energy loss. Biot-Savart law, Ampere’s law, Questions: Q 1. Two solenoids have 500 and 800 turns of wire and are placed co-axially close to each other. A current of 5.0 A in the first solenoid produces an average flux of 200μWb200\mu Wb200μWb though its each turn and

Magnetic shell, uniformly magnetized sphere; Ferromagnetic materials, hysteresis, energy loss. Biot-Savart law, Ampere’s law, Questions: Q 1. State Biot-Savart law. Calculate the magnitude of axial magnetic induction due to a circular loop of area A carrying current I. [15 marks] Q 2. A uniformly magnetised sphere of radius RRR has magnetization M⃗=M0z^\vec M=M_0\hat zM=M0​z^. If

 Dielectrics, polarization; Solutions to boundary-value problems-conducting and dielectric spheres in a uniform electric field;  Questions: Q 1. A region 1, z<0z<0z<0, has a dielectric material with ϵr=3.2\epsilon_r=3.2ϵr​=3.2 and a region 2, z>0z>0z>0 has a dielectric material with ϵr=2.0\epsilon_r=2.0ϵr​=2.0. Let the displacement vector in the region 1 be, D⃗1=−30ax+50ay+70aznCm−2\vec D_1 = -30a_x+50a_y+70a_z nCm^{-2}D1​=−30ax​+50ay​+70az​nCm−2. Assume the interface

Method of images and its applications; Potential and field due to a dipole, force and torque on a dipole in an external field; Questions: Q 1. A vertical oriented electric dipole having dipole moment p⃗\vec pp​ is kept at a height hhh above an infinitely large horizontal conducting plate, which is grounded as shown in

Laplace and Poisson equations in electrostatics and their applications; Energy of a system of charges, multiple expansion of scalar potential Questions: Q 1. Starting from the Laplace’s equation in a cylindrical polar coordinate system and using the method of separation of variables , obtain the differential equations for the solution of  r, θ\thetaθ  and z