Physical Chemistry , 1st ed.

troscopy. In MR spectroscopy, an experimenter has the opportunity to vary

both the electromagnetic radiation and the magnetic field strength until the

difference between the split energy levels equals the energy of the photon and

so a photon is absorbed: that is, a resonance is established. The two major

forms of MR spectroscopy are nuclear magnetic resonance and electron spin

resonance (also called electron paramagnetic resonance, depending on the type

of atomic or molecular system). As their names suggest, one deals with mag-

netic field interactions with the nucleus and the other deals with magnetic field

interactions with the electrons. Different and useful information can be ob-

tained with both.

16.2 Magnetic Fields, Magnetic Dipoles, and Electric Charges

Classically,magnetic fields(more formally called “magnetic inductions”) are

caused by moving charges. If a current Iwere flowing through a wire in one

direction, then the magnetic field is a circular vector mapping out a cylinder

around the wire and having its center at the wire, as in Figure 16.1. The mag-

netic field strength depends on the distance, labeled r, from the wire. The

magnitude of the magnetic field strength vector, labeled B, is given by the

equation

BB

2





0 I

r

 (16.1)

where the symbols are used to indicate the magnitude of a vector and  0 is

a physical constant called the permeability of a vacuum.Its value is 4 10 ^7

teslameter/ampere, or Tm/amp. The teslais one unit of magnetic field

strength, and is named after the erratic scientific genius Nikola Tesla (Figure

16.2). In terms of basic units, a tesla is equal to a kg/(coulombs). There is an-

other unit of magnetic field strength, the gauss,abbreviated G, which is equal

to 10^4 T.

The direction of the magnetic field vector is given by the “right-hand rule”:

if you point your right hand’s thumb in the direction of the current, the right

hand’s fingers would curl in the direction of the magnetic field. This is illus-

trated in Figure 16.3.

Conversely, consider an electrical current Ithat is going around in a circle,

a closed loop, as in Figure 16.4. This loop has some area, labeled A. According

to the classical theory of electromagnetism, this loop of current induces a lin-

ear magnetic effect called a magnetic dipole.It is called a dipole because it is a

vector that has a specific direction, which is normally considered the “positive”

or “north” pole of the dipole (the direction the vector is fromis considered the

“negative” or “south” pole). For the magnetic dipole vector, labeled , the mag-

nitude is

IA (16.2)

The unit of the magnetic dipole is amperemeter^2. The direction of the mag-

netic dipole vector is also given by the right-hand rule. If you curl your fingers

around the closed loop in the direction of the current, your thumb points in

the direction of the magnetic dipole vector (that is, toward the north pole end).

The magnetic dipole vector and the right-hand rule are illustrated in Figure

16.4. At this point, you should be able to differentiate between a magnetic field

and a magnetic dipole. They are two different things.

16.2 Magnetic Fields, Magnetic Dipoles, and Electric Charges 561

Current

Straight wire

B

Figure 16.2 Nikola Tesla (1856–1943) was

born in Croatia and emigrated to the United

States in 1884. Although he ultimately turned into

a rather eccentric character, his work in electric-

ity and magnetism almost earned him the 1912

Nobel Prize. He helped pioneer the use of alter-

nating current (AC) over direct current (DC) in

the fledgling electrical power industry.

Figure 16.1 Current traveling through a

straight wire causes the formation of a cylindri-

cal magnetic field, labeled B.

Current

B

Figure 16.3 The right-hand rule is used to de-

termine the direction of the magnetic field vec-

tors. If the thumb of the right hand is pointed in

the direction of the current, the fingers curl in the

direction of the magnetic field, as shown.

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