Electricity and Magnetism Answers

The expression of the magnetic field associated with an electromagnetic wave in
vacuum is given by
B = (100T) y sin ( 2π × 10^8t + kz)
Determine the wave number, frequency and the direction of propagation of the wave,
and the magnitude and direction of the electric field associated with it.

Using Maxwell’s equations in vacuum, derive the wave equation for the z-component
of the electric field vector associated with an electromagnetic wave.

What rate of change of current in a solenoid having self-inductance 19.4 mH produces a self-induced emf of 100 mV in it?

A long, straight wire of diameter 5.0 mm carries a uniformly distributed current of
15 A. At what distance from the axis of the wire will the magnitude of B be maximum? Justify your answer.

A wire loop of resistance
10 ohm and radius 10 cm is kept in the plane of this paper in a uniform magnetic field B.
The direction of B is perpendicular to the
plane of the page and points out of it and its magnitude is increasing at the rate of 0.50T/s.
Determine the magnitude and direction of the induced current in the loop.

Calculate the magnitudes of magnetic intensity
H and the magnetic field B at the centre of a 1500-turn solenoid which is 0.22 m long and carries a current of
1.5 A.

A long, straight wire of diameter 5.0 mm carries a uniformly distributed current of
15 A. At what distance from the axis of the wire will the magnitude of
B

be
maximum? Justify your answer

A 0.5 m length of current-carrying wire kept perpendicular to a magnetic field of
magnitude 200 mT experiences a force of 1.5 mN. What is the current flowing in the
wire.

A dielectric of dielectric constant 2.5 is filled in the gap between the plates of a
capacitor. Calculate the factor by which the capacitance is increased, if the
dielectric is only sufficient to fill up one-fourth of the gap

Define electric displacement vector
D

and deduce Gauss’s law for dielectrics