Chapter 33. The Magnetic Field
Digital information is stored
on a hard disk as
microscopic patches of
magnetism. Just what is
magnetism? How are
magnetic fields created?
What are their properties?
These are the questions we
will address.
Chapter Goal: To learn how
to calculate and use the
magnetic field.
Chapter 33. The Magnetic Field
Topics:
• Magnetism
• The Discovery of the Magnetic Field
• The Source of the Magnetic Field: Moving Charges
• The Magnetic Field of a Current
• Magnetic Dipoles
• Ampère’s Law and Solenoids
• The Magnetic Force on a Moving Charge
• Magnetic Forces on Current-Carrying Wires
• Forces and Torques on Current Loops
• Magnetic Properties of Matter
Stop to think 33.1
page 1000
Stop to think 33.2
page 1002
Stop to think 33.3
page 1005
Stop to think 33.4
page 1012
Stop to think 33.5
page 1021
Stop to think 33.6
page 1028
Stop to think 33.7
page 1031
Tactics: Right-hand rule for fields
The Source of the Magnetic Field:
Moving Charges
The magnetic field of a charged particle q moving with
velocity v is given by the Biot-Savart law:
where r is the distance from the charge
and θ is the angle between v and r. μ0 is
permeability constant =4π×10-7 Tm/A
The Biot-Savart law can be written in
terms of the cross product as
The Magnetic Field of a Current
The magnetic field of a long, straight wire carrying
current I, at a distance d from the wire is
See textbook P1007
The magnetic field at the center of a coil of N turns
and radius R, carrying a current I is
See textbook P1008
0
IR2
Bloop 
2 ( z 2  R2 )3/ 2
The strength of the uniform magnetic field inside a
solenoid is
where n = N/l is the number of turns per unit length.
EXAMPLE 33.4 The magnetic field strength near
a heater wire
QUESTION:
EXAMPLE 33.4 The magnetic field
strength near a heater wire
Magnetic Dipoles
The magnetic dipole
moment of a current loop
enclosing an area A is
defined as
The SI units of the magnetic
dipole moment are A m2.
The on-axis field of a
magnetic dipole is
See textbook P1011
The Magnetic Force on a Moving
Charge
The magnetic force on a charge q as it
moves through a magnetic field B with
velocity v is
where α is the angle
between v and B.
Magnetic forces on moving charges
Cyclotron motion
e
2
v
F  qvB  mar  m
Tcyc
2 r 2 m


v
qB
r
 rcyc
mv

qB
Force between two parallel wires
0 I
B
2 d
0lI1I 2
F  I1lB2 
2 d
  IA
Is magnetic dipole moments
  B
What is the current direction in the loop?
A. Out of the page at the top of the loop, into
the page at the bottom.
B. Out of the page at the bottom of the
loop, into the page at the top.
An electron moves perpendicular to
a magnetic field. What Bis the
direction of B
A.
B.
C.
D.
E.
Left
Into the page
Out of the page
Up
Down
What is the current
direction in this loop?
And which side of the
loop is the north pole?
A.
B.
C.
D.
Current counterclockwise, north pole on bottom
Current clockwise; north pole on bottom
Current counterclockwise, north pole on top
Current clockwise; north pole on top