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MOTION IN PHYSICS
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Chapter EightELECTROMAGNETIC
WAVES
8.1 INTRODUCTION
In Chapter 4, we learnt that an electric current produces magnetic field
and that two current-carrying wires exert a magnetic force on each other.
Further, in Chapter 6, we have seen that a magnetic field changing with
time gives rise to an electric field. Is the converse also true? Does an
electric field changing with time give rise to a magnetic field? James Clerk
Maxwell (1831-1879), argued that this was indeed the case – not only
an electric current but also a time-varying electric field generates magnetic
field. While applying the Ampere’s circuital law to find magnetic field at a
point outside a capacitor connected to a time-varying current, Maxwell
noticed an inconsistency in the Ampere’s circuital law. He suggested the
existence of an additional current, called by him, the displacement
current to remove this inconsistency.
Maxwell formulated a set of equations involving electric and magnetic
fields, and their sources, the charge and current densities. These
equations are known as Maxwell’s equations. Together with the Lorentz
force formula (Chapter 4), they mathematically express all the basic laws
of electromagnetism.
The most important prediction to emerge from Maxwell’s equations
is the existence of electromagnetic waves, which are (coupled) time-
varying electric and magnetic fields that propagate in space. The speed
of the waves, according to these equations, turned out to be very close to
Rationalised 2023-24
, Physics
the speed of light( 3 ×108 m/s), obtained from optical
measurements. This led to the remarkable conclusion
that light is an electromagnetic wave. Maxwell’s work
thus unified the domain of electricity, magnetism and
light. Hertz, in 1885, experimentally demonstrated the
existence of electromagnetic waves. Its technological use
by Marconi and others led in due course to the
revolution in communication that we are witnessing
today.
In this chapter, we first discuss the need for
displacement current and its consequences. Then we
present a descriptive account of electromagnetic waves.
James Clerk Maxwell The broad spectrum of electromagnetic waves,
(1831 – 1879) Born in stretching from g rays (wavelength ~10–12 m) to long
Edinburgh, Scotland,
radio waves (wavelength ~106 m) is described.
was among the greatest
physicists of the
nineteenth century. He 8.2 DISPLACEMENT CURRENT
derived the thermal We have seen in Chapter 4 that an electrical current
velocity distribution of
produces a magnetic field around it. Maxwell showed
molecules in a gas and
was among the first to that for logical consistency, a changing electric field must
obtain reliable also produce a magnetic field. This effect is of great
estimates of molecular importance because it explains the existence of radio
parameters from waves, gamma rays and visible light, as well as all other
measurable quantities forms of electromagnetic waves.
like viscosity, etc.
To see how a changing electric field gives rise to
JAMES CLERK MAXWELL (1831–1879)
Maxwell’s greatest
acheivement was the a magnetic field, let us consider the process of
unification of the laws of charging of a capacitor and apply Ampere’s circuital
electricity and law given by (Chapter 4)
magnetism (discovered
by Coulomb, Oersted, “B.dl = m0 i (t ) (8.1)
Ampere and Faraday)
to find magnetic field at a point outside the capacitor.
into a consistent set of
equations now called Figure 8.1(a) shows a parallel plate capacitor C which
Maxwell’s equations. is a part of circuit through which a time-dependent
From these he arrived at current i (t ) flows . Let us find the magnetic field at a
the most important point such as P, in a region outside the parallel plate
conclusion that light is capacitor. For this, we consider a plane circular loop of
an electromagnetic radius r whose plane is perpendicular to the direction
wave. Interestingly,
of the current-carrying wire, and which is centred
Maxwell did not agree
with the idea (strongly symmetrically with respect to the wire [Fig. 8.1(a)]. From
suggested by the symmetry, the magnetic field is directed along the
Faraday’s laws of circumference of the circular loop and is the same in
electrolysis) that magnitude at all points on the loop so that if B is the
electricity was magnitude of the field, the left side of Eq. (8.1) is B (2p r).
particulate in nature. So we have
B (2pr) = m0i (t ) (8 .2)
202
Rationalised 2023-24
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