Page 16 - Electromagnetics

1.2 The field concept of electromagnetics
Introductory treatments of electromagnetics often stress the role of the field in force
transmission:the individual fields E and B are defined via the mechanical force on a
small test charge. This is certainly acceptable, but does not tell the whole story. We
might, for example, be left with the impression that the EM field always arises from
an interaction between charged objects. Often coupled with this is the notion that the
field concept is meant merely as an aid to the calculation of force, a kind of notational
convenience not placed on the same physical footing as force itself. In fact, fields are
more than useful — they are fundamental. Before discussing electromagnetic fields in
more detail, let us attempt to gain a better perspective on the field concept and its role
in modern physical theory. Fields play a central role in any attempt to describe physical
reality. They are as real as the physical substances we ascribe to everyday experience.
In the words of Einstein [63],

“It seems impossible to give an obvious qualitative criterion for distinguishing between
matter and field or charge and field.”
We must therefore put fields and particles of matter on the same footing:both carry
energy and momentum, and both interact with the observable world.

1.2.1 Historical perspective

Early nineteenth century physical thought was dominated by the action at a distance
concept, formulated by Newton more than 100 years earlier in his immensely successful
theory of gravitation. In this view the influence of individual bodies extends across space,
instantaneously affects other bodies, and remains completely unaffected by the presence
of an intervening medium. Such an idea was revolutionary; until then action by contact,in
which objects are thought to affect each other through physical contact or by contact with
the intervening medium, seemed the obvious and only means for mechanical interaction.
Priestly’s experiments in 1766 and Coulomb’s torsion-bar experiments in 1785 seemed to
indicate that the force between two electrically charged objects behaves in strict analogy
with gravitation:both forces obey inverse square laws and act along a line joining the
objects. Oersted, Ampere, Biot, and Savart soon showed that the magnetic force on
segments of current-carrying wires also obeys an inverse square law.
The experiments of Faraday in the 1830s placed doubt on whether action at a distance
really describes electric and magnetic phenomena. When a material (such as a dielec-
tric) is placed between two charged objects, the force of interaction decreases; thus, the
intervening medium does play a role in conveying the force from one object to the other.
To explain this, Faraday visualized “lines of force” extending from one charged object to
another. The manner in which these lines were thought to interact with materials they
intercepted along their path was crucial in understanding the forces on the objects. This
also held for magnetic effects. Of particular importance was the number of lines passing
through a certain area (the flux), which was thought to determine the amplitude of the
effect observed in Faraday’s experiments on electromagnetic induction.
Faraday’s ideas presented a new world view:electromagnetic phenomena occur in the
region surrounding charged bodies, and can be described in terms of the laws governing
the “field” of his lines of force. Analogies were made to the stresses and strains in material
objects, and it appeared that Faraday’s force lines created equivalent electromagnetic

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