# chapt08 - CHAPTER 8 THE STEADY MAGNETIC FIELD At this point...

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CHAPTER 8 THE STEADY MAGNETIC FIELD At 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 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 which 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 shall begin our study of the magnetic field with a definition of the magnetic field itself and show how it arsies from a current distribution. The effect of this field on other currents, or the second half of the physical problem, will be discussed in the following chapter. As we did with the electric field, we shall confine our initial discussion to free-space conditions, and the effect of material media will also be saved for discussion in the following chapter. 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 shall find it neces- sary to accept several laws temporarily on faith alone, relegating their proof to 224

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the (rather difficult) final section in this chapter. This section may well be omitted when studying magnetic fields for the first time. It is included to make acceptance of the laws a little easier; the proof of the laws does exist and is available for the disbelievers or the more advanced student. 8.1 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 shall largely ignore the permanent magnet and save the time-varying electric field for a later discussion. Our present relationships will concern the magnetic field produced by a differ- ential dc element in free space. We may think of this differential current element as a vanishingly small section of a current-carrying filamentary conductor, where a filamentary con- ductor is the limiting case of a cylindrical conductor of circular cross section as the radius approaches zero. We assume a current I flowing in a different vector length of the filament d L . The law of Biot-Savart 1 then states that at any point P the magnitude of the magnetic field intensity produced by the differential ele- ment is proportional to the product of the current, the magnitude of the differ- ential length, and the sine of the angle lying between the filament and a line connecting the filament to the point P at which the field is desired; also, the magnitude of the magnetic field intensity is inversely proportional to the square
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chapt08 - CHAPTER 8 THE STEADY MAGNETIC FIELD At this point...

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