An electric field given by E i 3 4k acts in a region of space. Calculate the electric flux due to this electric field through the surface of area 0·1 m^2 lying in the x-y plane.

Show that the work done by the electric field around a closed path is zero.

Show that the energy per unit volume stored in the electrostatic field of a parallel-plate capacitor with free space as the intervening medium is given by

U

A long solenoid of length area of cross-section A and having nI turns has wound around its centre a small coil having n2 turns. Calculate the mutual inductance between the solenoid and the coil.

A magnetic material placed in an external magnetic field has a magnetization of 3300 and flux density of 0·0044 T. Calculate the magnetizing field, H.

State Gauss's law for magnetism. Discuss the physical meaning of this law.

Three charges q and 2q are situated on the vertices of an equilateral triangle of side a. Calculate the electrostatic potential energy of this system of charges,

when q 2x 10^-5C and a 10cm.

Show that the energy expended in establishing a current I in a coil of self-inductance L is 1/2 Li^2.


Establish the relation V x E dB/dt where the symbols have their usual meanings.

Starting from Maxwell's equations for electromagnetic field, obtain the wave equation for the electric field in a homogeneous and isotropic dielectric medium.

An electron having velocity 3 x 10^7 enters a magnetic field of magnitude 2·0 x Tat an angle of 30° with it. Calculate

radius of the helical path, and

time taken by the electron for one revolution. 1·76 x 10^11 C

Two similar coils of wire having a radius of 7 cm and 60 turns have a common axis and are 18 cm apart. Calculate the magnetic field at a point midway between the coils on their common axis, when a current of 0·1 A is passed through them in the same direction.

Define electric potential. Obtain an expression for the electrostatic potential energy of a system of n-point charges.

A dielectric slab of thickness 0·01 m and dielectric constant 5 is placed between the plates of a parallel-plate capacitor. The area of each plate is 2x mand they are 0·02 m apart. Calculate

capacitance of the capacitor, and

by what distance the separation between the plates has to be increased to restore the capacitance to its original value (when there is no dielectric between plates).

Use Gauss's law to derive the expression for the electric field due to a uniformly charged solid conducting sphere at a point lying

inside, and

outside the sphere.

State Biot -Savart's law. Use this law to derive an expression for the magnetic field at a point lying on the axis of a current-carrying circular coil.