Download 892 29.7

7.5 mV. A potential difference of this magnitude is readily measured.
Chapter 29
Magnetic Fields
Summary
Definition
S
The magnetic dipole moment m
of a loop carrying a current I is
S
S
; IA
m
S
(29.15)
S
where the area vector A is perpendicular to the plane of the loop and 0 A 0 is equal to the area of the loop. The SI unit
S
of m
is A ? m2.
Concepts and Principles
If a charged particle moves in a uniform magnetic field so that its initial velocity is perpendicular to the field, the
particle moves in a circle, the plane of which is perpendicular to the magnetic field. The radius of the circular path is
r5
mv
qB
(29.3)
where m is the mass of the particle and q is its charge. The angular speed of the charged particle is
v5
If a straight conductor of length L carries a current
I, the force exerted on that conductor when it is placed
S
in a uniform magnetic field B is
S
S
S
qB
m
(29.4)
If an arbitrarily shaped wire carrying a current I is
placed in a magnetic field, the magnetic force exerted
on a very small segment d S
s is
S
S
S
d FB 5 I d S
s 3 B
(29.10)
FB 5 I L 3 B
(29.11)
where the direction of L is in the direction of the curS
rent and 0 L 0 5 L.
To determine the total magnetic force on the wire, one
must integrate Equation 29.11 over the wire, keeping
S
in mind that both B and d S
s may vary at each point.
The torque S
t on a current loop placed in a uniform
S
magnetic field B is
The potential energy of the system of a magnetic
dipole in a magnetic field is
S
S
S
t5m
3 B
893
(29.18)
S
S Questions
UBObjective
5 2m
?B
(29.17)
Analysis Models for Problem Solving
Particle in a Field (Magnetic) A source (to be discussed in Chapter 30) establishes a
S
magnetic field B throughout space. When a particle with charge q and moving with velocity
S
v is placed in that field, it experiences a magnetic force given by
S
S
v 3 B
FB 5 q S
z
S
(29.1)
q
The direction of this magnetic force is perpendicular both to the velocity of the particle and
to the magnetic field. The magnitude of this force is
FB 5 0 q 0 vB sin u
S
S
(29.2)
S
S
v
x
where u is the smaller angle between v and B . The SI unit of B is the tesla (T), where 1 T 5 1 N/A · m.
Objective Questions
1. denotes answer available in Student Solutions Manual/Study Guide
Objective Questions 3, 4, and 6 in Chapter 11 can be
assigned with this chapter as review for the vector product.
1. A spatially uniform magnetic field cannot exert a
#
S
v
S
S
FB ! q v " B
S
B
y