Physical Chemistry Third Edition

1002 24 Magnetic Resonance Spectroscopy

24.1 Magnetic Fields and Magnetic Dipoles

Any electric current produces a magnetic field, which is a vector quantity. The strength

of a magnetic field is specified by themagnetic inductionBor by themagnetic field

strength H. These two vector quantities are proportional to each other. We will generally

use the magnetic inductionBand will follow the common terminology of chemists and

call it themagnetic field.Ampère’s lawgives the magnitude of the magnetic field in

a vacuum at a perpendicular distancerfrom a long straight wire carrying an electric

currentI:

B|B|

μ 0 I

2 πr

(24.1-1)

whereμ 0 is thepermeabilityof a vacuum, defined by

μ 0  4 π× 10 −^7 TmA−^1 (exactly, by definition) (24.1-2)

The conventional direction of an electric current is the apparent direction of motion

of positive charges. In a current of electrons, the electrons are moving in the opposite

direction. If we construct a circle of radiusrthat is centered on the wire and is per-

pendicular to the wire, the magnetic field is tangent to the circle at any point on the

circle, and its magnitude is given by Eq. (24.1-1). The direction can be obtained from

aright-hand rule: If the thumb of the right hand points in the direction of the current,

the curled fingers point in the direction of the magnetic field. If the current is measured

in amperes (denoted by A and equal to coulombs per second) and the distance is mea-

sured in meters, then the magnetic field is measured in tesla (T). There is another unit

of magnetic field called thegauss, defined by

10000 gauss1 T (exactly) (24.1-3)

The magnitude of the earth’s magnetic field is somewhat less than 1 gauss at most

locations on the earth’s surface.

Andre-Marie Ampère, 1775–1836, was
a great French physicist who was
largely responsible for the founding of
the science of electromagnetism. He
was a child prodigy who is said to have
worked out complicated mathematical
sums using pebbles before he knew the
symbols for the numbers. The unit of
electrical current is named for him.

The tesla is named for Nikola Tesla,
1856–1943, an eccentric
Austrian-American electrical engineer
and inventor who came to the United
States in 1884 to work with Thomas
Edison, but who soon parted with him
and went to Westinghouse, because
Edison favored direct current for
municipal power grids but Tesla favored
alternating current.

The direction of an electric current was
defined by Benjamin Franklin,
1706–1790, American politician, printer,
inventor, and self-taught physicist, who
gained fame for many things, including
showing that lightning is a transfer of
electric charge and inventing the
lightning rod. He also originated the
designation of the two kinds of electric
charge as positive and negative.

EXAMPLE24.1

If a long straight wire is carrying a direct current of 15.0 A, find the magnitude of the magnetic

field at a location 0.050 m from the wire. If the wire is vertical and the current is flowing

upward (electrons flowing downward) and the location is due east of the wire, what is the

direction of the magnetic field?

Solution

B

μ 0 I

2 πr



(4π× 10 −^7 TmA−^1 )(15.0A)

2 π(0.050 m)

 6. 0 × 10 −^5 T 0 .60 gauss

By the right-hand rule, the direction is due north. This magnetic field is roughly equal to the

earth’s magnetic field at the surface of the earth.

Exercise 24.1

a.What is the direction of the magnetic field in the previous example if the location is due south

of the wire?