Solution: Electromagnetic waves are by nature transverse to the direction
of propagation of (i) oscillation of electric field and
(ii) oscillation of magnetic field, which are mutually perpendicular to
each other. The direction of propagation of the wave is perpendicular to
electric and magnetic fields.
Solution: A stationary charge has an electric field around it but no
magnetic field. When given an impulse, it begins to move with the
production of electric and magnetic fields. When the charge moves with a
constant velocity, the magnetic field does not change with time, hence it
cannot produce an electric field. As the charge is accelerated, both
electric and magnetic fields change with time and space, one becoming a
source of the other and giving rise to an electromagnetic wave.
Solution: Some of the chief characteristics of electromagnetic waves are:
(i) In an electromagnetic wave, the directions of oscillation of the
electric and magnetic fields are perpendicular to each other as well
as to the direction of propagation of the wave.
(ii) The speed of an electromagnetic wave in space is about 3 ´
108 m/s while in any other medium, it depends on the electric
and magnetic properties of the medium and not on the amplitude of the
(iii) The electric and magnetic field variations are in phase, i.e.
both attain their maxima and minima at the same rime and place.
Solution: Not all the quantities appearing in these equations have
dimensions assigned to them from 'outside' (i.e., from independent
equations and definitions). Some of the dimensions have to be fixed up
from a few of the equations themselves, and the remaining equations (or
terms in the equations) can then be checked for dimensional consistency.
The dimensions of eo is given from
Coulomb's law to be
=C2 N-1 m-2
The dimensions of E is fixed by its definition as force per unit charge
Solution: Let us consider a stationary electric charge. At some distance
from this charge, there will be an electric field but no magnetic field.
When the charge begins to move, there will be both electric and magnetic
fields at P. If in a region of space, there is a flux of magnetic field
varying with time, it gives rise to an emf (Faraday's law of
electromagnetic induction). Applying this law to a small region, say a
small square perpendicular to the direction of the magnetic field, it can
be shown that the electric fields along the two parallel sides of the
square are not the same. Thus a time dependent magnetic field gives rise
to an electric field that varies with position. Now suppose that the
electric field depends on time as well. Then from Maxwell's generalization
of Ampere's circuital law, such an electric field produces a magnetic
field. So, we find that electric and magnetic fields that depend on space
and time produce and sustain each other. A simple form of such a
continuing change is a wave. In a plane wave, for example, the electric
and magnetic fields vary sinusoidally with distance at a given time, and
with time at a given point. Thus, an oscillating charge, which has
non-zero acceleration, will continuously emit electromagnetic waves.