Physical Chemistry , 1st ed.

Currents consist of individual electrical charges, usually electrons. We can

therefore consider the magnetic fields produced by a single electron as it

moves—at least classically.

Example 16.1

For a distance of 1 m from a single straight wire, calculate the magnetic field

produced by each of the following:

a.A single electron passing by a point each second

b.A mole of electrons passing by a point each second

Solution

a.At 1.602  10 ^19 coulombs per electron, the current Iin this case is

1.602  10 ^19 C/s, or 1.602  10 ^19 amp. Substituting into equation 16.1,

one gets

B3.204  10 ^26 T

b.One mole of electrons has a charge of approximately 96,500 C (this is

Faraday’s constant) for a current of 96,500 amps. (In reality, such a current

would probably destroy the wire.) Substituting this value into equation 16.1:

B0.0193 T

Compare the answer from part b to the value for Earth’s natural magnetic

field, which is approximately 0.6 gauss, or 6  10 ^5 T. Common currents

around the home, office, or lab are 15 to 30 amperes, so the magnetic fields to

which one might be exposed from normal electrical wiring are on the order of

magnitude of Earth’s own magnetic field.

Example 16.2

Calculate the magnetic dipole magnitude of the following:

a.1 ampere of charge in a superconducting ring having a radius of 0.500 m

b.A current of 6.58  1015 amperes moving about a ring having a radius of

0.529Å. (This is equivalent to an electron in the first Bohr radius of the Bohr

hydrogen atom.)

Solution

a.The area of the circle is r^2 (3.14159)(0.5 m)^2 0.785 m^2. Therefore,

the magnetic dipole for 1 ampere at 0.5 m radius is 0.785 ampm^2.

b.The area of this smaller ring is (0.529  10 ^10 m)^2 2.80  10 ^21 m^2.

The magnetic dipole in this case is simply (6.58  1015 amp) (2.80 

10 ^21 m^2 ) 1.84  10 ^5 ampm^2. [Although this is a smaller magnetic di-

pole than that in part a, it is due to a single (classical) electron.]

Magnetic effects like fields and dipoles interact with each other. It’s like two

bar magnets interacting, either both north or south poles interacting to repel

each other, or a north and a south pole of a magnet attracting each other. A

potential energy defines their interaction (a repulsive potential energy or an

attractive potential energy, respectively: see Figure 16.5). It is the same with a

(4 10 ^7 Tm/amp)(96,500 amp)



2 (1 m)

(4 10 ^7 Tm/amp)(1.602  10 ^19 amp)



2 (1 m)

562 CHAPTER 16 Introduction to Magnetic Spectroscopy

Current

Magnetic

dipole, 

Loop of wire
having area
A  r^2

r

Figure 16.4 Current in a loop causes the for-
mation of a magnetic dipole, which is different
from a magnetic field. However, the right-hand
rule is also used to determine the direction of the
magnetic dipole, as shown.