Electricity and Magnetism Answers

Explain the physical significance of the Maxwell’s equation.
Derive the wave equation for the z-component of the electric field of an
electromagnetic wave.

A sinusoidal plane electromagnetic wave propagates from water (nw =1.33) to glass
(ng = 1.5). Calculate the reflection and transmission coefficients for this wave at the
interface of the two media. Show that when an electromagnetic wave enters from
one dielectric medium to the other, its frequency remains unchanged.

An electric generator comprises a square wire loop of side 100 cm. The loop has
50 turns and is placed in a magnetic field of 0.5T. By what frequency should this
loop be rotated in the magnetic field to produce an AC voltage of peak value 250 V?

Establish the relation B = μ0 (H + M) for a ferromagnetic material.

How do we differentiate between diamagnetic and paramagnetic materials? Show
that for diamagnetic atoms placed in an external magnetic field B, the change in
dipole moment is opposite to the direction of B.

A 10 eV electron is circulating in a plane at right angles to a uniform magnetic field
of 1.0 × 10−4 T. Calculate the orbital radius of the electron, cyclotron frequency,
period of revolution, and the direction of circular motion of the electron as viewed
by an observer looking along the magnetic field.

A copper wire of diameter 1 mm and length 30 m is connected across a battery of
2V. Calculate the current density in the wire and drift velocity of the electrons. The
resistivity of copper is 1.72 × 10−8 Wm and n = 8.0 × 1028 electrons m−3.

A glass of relative permittivity 4 is kept in an external electric field of magnitude
102 Vm−1. Calculate the polarisation vector, molecular/atomic polarisability and the
refractive index of the glass.

The capacitance of a parallel plate capacitor is increased by a factor of 5 when a
dielectric material fills the space between its plates. What is the relative permitivity
of the dielectric material? If this material is placed in between the plates of a
cylindrical capacitor of outer and inner radii 12 cm and 10 cm respectively,
calculate the capacitance per unit length of the cylindrical capacitor.

What do you understand by electrostatic potential energy? Calculate the
electrostatic potential energy for the system of charges shown below. Take q = 4μC
and a = 2 cm.