Page 198 - Engineering Electromagnetics, 8th Edition

7 CHAPTER

The Steady Magnetic Field

t this point, the concept of a field should be a familiar one. Since we first
accepted the experimental law of forces existing between two point charges
A and defined electric field intensity as the force per unit charge on a test charge
in the presence of a second charge, we have discussed numerous fields. These fields
possess no real physical basis, for physical measurements must always be in terms
of the forces on the charges in the detection equipment. Those charges that are the
source cause measurable forces to be exerted on other charges, which we may think
of as detector charges. The fact that we attribute a field to the source charges and then
determine the effect of this field on the detector charges amounts merely to a division
of the basic problem into two parts for convenience.
We will begin our study of the magnetic field with a definition of the magnetic
field itself and show how it arises from a current distribution. The effect of this field
on other currents, or the second half of the physical problem, will be discussed in
Chapter 8. As we did with the electric field, we confine our initial discussion to free-
space conditions, and the effect of material media will also be saved for discussion
in Chapter 8.
The relation of the steady magnetic field to its source is more complicated than
is the relation of the electrostatic field to its source. We will find it necessary to
accept several laws temporarily on faith alone. The proof of the laws does exist and
is available on the Web site for the disbelievers or the more advanced student. ■

7.1 BIOT-SAVART LAW
The source of the steady magnetic field may be a permanent magnet, an electric field
changing linearly with time, or a direct current. We will largely ignore the permanent
magnet and save the time-varying electric field for a later discussion. Our present study
will concern the magnetic field produced by a differential dc element in free space.
We may think of this differential current element as a vanishingly small section of
acurrent-carryingfilamentaryconductor,whereafilamentaryconductoristhelimiting

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