Physical Chemistry Third Edition

24.1 Magnetic Fields and Magnetic Dipoles 1003

b.What is the direction and magnitude of the magnetic field at a location 0.100 m due west of

the wire?

If a particle of chargeQis moving with velocityvthrough a magnetic fieldB, there

is a force on the particle given by

FQv×B (24.1-4)

where×stands for the vector product (cross product) of the two vectors, which

is discussed in Appendix B. There is a screw-thread rule for the cross product. If

the vector on the left is rotated through an angle no greater than 180◦to point in

the direction of the second vector, the cross product points in the direction that a

right-handed screw would move. The force on a positive charge is in this direction.

The force on a negative charge is in the opposite direction.

EXAMPLE24.2

If an electron (Q−e− 1. 602 × 10 −^19 C) is located due east of the wire in

Example 24.1 at a distance of 0.050 m from the wire and is moving east at a speed of

145ms−^1 , find the direction and the magnitude of the force on the electron direction.

Solution

From Eq. (B.3-38) in Appendix B and the fact thatvandBare perpendicular to each other,

F|F|Q|v×B|Q|v||B|sin(α)Q|v||B|

(− 1. 602 × 10 −^19 C)(145 m s−^1 )(6. 0 × 10 −^5 T)

(− 1. 602 × 10 −^19 C)(145 m s−^1 )(6. 0 × 10 −^5 NsC−^1 m−^1 )

 1 .39 N

where we have deduced the fact that the tesla unit must be equivalent to N s C−^1 m−^1 ,or

NA−^1 m−^1 ,orkgs−^1 C−^1. The direction of the force is downward by the screw-thread

rule.

Exercise 24.2

a.If an electron (Q−e− 1. 602 × 10 −^19 C) is located due east of the wire in Exercise 24.1

at a distance of 0.050 m from the wire and is moving north at a speed of 145 m s−^1 , find the

direction and the magnitude of the force on the electron.

b.If the electron is in the position of part a but is moving directly toward the wire, find the

direction and the magnitude of the force on the electron.

Magnetic Dipoles

Magnetic dipoles are like bar magnets or compass needles with a “north-seeking” pole

at one end and a “south-seeking” pole at the other. A magnetic field applies a torque

(turning force) on a magnetic dipole, much as an electric field applies a torque to an

electric dipole. An electric dipole can be made up of a positive and a negative charge