chapter 30
Sources of the Magnetic Field
30.1 The Biot–Savart Law
30.2 The Magnetic Force Between Two Parallel
Conductors
30.3 Ampère’s Law
30.4 The Magnetic Field of a Solenoid
30.5 Gauss’s Law in Magnetism
30.6 Magnetism in Matter
In Chapter 29, we discussed the magnetic
force exerted on a charged particle moving in
a magnetic field. To complete the description of
the magnetic interaction, this chapter explores
the origin of the magnetic field, moving charges.
We begin by showing how to use the law of Biot
and Savart to calculate the magnetic field produced
at some point in space by a small current
element. This formalism is then used to calculate
the total magnetic field due to various current
distributions. Next, we show how to determine
the force between two current-carrying conductors,
leading to the definition of the ampere. We
also introduce Ampère’s law, which is useful in calculating the magnetic field of a highly
symmetric configuration carrying a steady current.
This chapter is also concerned with the complex processes that occur in magnetic
materials. All magnetic effects in matter can be explained on the basis of atomic magnetic
moments, which arise both from the orbital motion of electrons and from an intrinsic
property of electrons known as spin.
chapter 30
Sources of the Magnetic Field
A cardiac catheterization laboratory stands ready to receive a patient
suffering from atrial fibrillation. The large white objects on either side of
the operating table are strong magnets that place the patient in a magnetic
field. The electrophysiologist performing a catheter ablation procedure
sits at a computer in the room to the left. With guidance from the magnetic
field, he or she uses a joystick and other controls to thread the magneticallysensitive
tip of a cardiac catheter through blood vessels and into the
chambers of the heart. (© Courtesy of Stereotaxis, Inc.)
30.1 The Biot–Savart Law
Shortly after Oersted’s discovery in 1819 that a compass needle is deflected by a
current-carrying conductor, Jean-Baptiste Biot (1774–1862) and Félix Savart (1791–