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Ch. 21 - Magnetic Forces and Fields
21.1 Magnetism
• Chinese scientists first used
the lodestone compass for
navigation in the 12th century.
• By the beginning of the 17th
century, Europeans
understood that compasses
worked because the Earth
itself was a magnet.
• Today we know this is due to
the interaction between the
solid and molten parts of the
Earth’s iron core.
21.1 Magnetic Fields
The behavior of magnetic
poles is similar to that of
like and unlike electric charges.
21.1 Magnetic Fields
The needle of a compass is permanent magnet that has a north
magnetic pole (N) at one end and a south magnetic pole (S) at
the other.
The north pole of a magnet is attracted to the south pole of another
magnet.
The geographic North Pole is actually a south magnetic pole.
21.1 Magnetic Fields
•Surrounding a magnet there is a magnetic field, an “alteration of
space” caused by the magnet.
•The direction of the magnetic field at any point in space is the
direction indicated by the north pole of a small compass needle
placed at that point.

•The variable we use for the magnetic field is B
•The SI unit for magnetic field strength is the (N-s)/(C-m), the tesla, T.
The Aurora Borealis (Northern Lights) and
Aurora Australis (Southern Lights) occur near
the poles, where the Earth’s magnetic field is
the strongest.
The compass and magnetic field lines
http://phet.colorado.edu/en/simulation/magnetsand-electromagnets
Magnetism
• An understanding of the
relationship between
electricity and magnetism
began in 1819 with work
by Oersted, who
discovered that an electric
current could influence a
compass needle.
• Later in the 19th century,
Faraday and Maxwell and
others unified electricity
and magnetism into the
study of electromagnetism.
An electromagnetic wave consists
of propogating electric (E) and
magnetic (B) fields.
Moving charge is a magnet and has a
magnetic field
http://phet.colorado.edu/en/simulation/magnetsand-electromagnets
3 D- visualization of vectors and
current
MAGNETIC FIELD OF A LONG, STRAIGHT WIRE
•The magnetic field due to a long
straight current-carrying wire is
circular in shape.
• The magnitude, (magnetic field
strength) is inversely proportional to
the distance from the wire. Spacing of
field lines increases with distance.
• The field strength is:
o I
B
2 r
Where μ0 the permeability of free
space, a fundamental constant of
magnetism:
o  4 10 7 T  m A
= 1.257 x 10-6 T m/A
B = (2 x 10-7)I
r
21.7 Magnetic Fields Produced by Currents
Right-Hand Rule No. 2. Curl the fingers of the
right hand into the shape of a half-circle. Point
the thumb in the direction of the conventional
current, and the tips of the fingers will point
in the direction of the magnetic field.
In what direction does the magnetic field
point at position P?
A. Up
B. Down C. Into the page
D. Out of the page
Finding the magnetic field strength, B
The long straight wire
carries a current
of 3.0 A. Determine the
magnitude of the magnetic
field at a distance of 0.050
m from the wire.
o I
B
2 r
Finding the magnetic field strength, B
The long straight wire
carries a current
of 3.0 A. Determine the
magnitude of the magnetic
field at a distance of 0.050
m from the wire.
B = 1.2 x 10-5 Tesla
Superposition of magnetic fields
Which statement is true?
A. The magnetic field is
equal at 1,2 and 3
B. The magnetic field is
0 at 2
C. The magnetic field is
greatest at 2
Superposition of magnetic fields
Calculate the magnetic
field strength and
direction at points 1,2,
and 3
Superposition of magnetic fields
Calculate the magnetic
field strength and
direction at points 1,2,
and 3.
B1 = 6.67 x 10-5 T out of
the page
B2 = 2 x 10-4 T into the
page
B3 = 6.67 x 10-5 T out of
the page
Worksheet
Current Loops are Magnets
The RHR2 (for fields)
shows the direction
of the magnetic field
in the center of the
wire.
http://phet.colorado.edu/en/si
mulation/magnets-andelectromagnets
The magnetic field of a current loop: 2
views
Comparison of fields of current
loop and magnet
A current loop is a magnet
• The magnetic field of the current loop exerts a force on
the poles of the bar magnet (and vice versa).
•The direction of the B field of loop:
• Direction of force:
•B field of bar magnet not shown
21.7 Magnetic Fields Produced by Currents
B field
Direction of force on
loops
A THIN LOOP OF WIRE
The magnetic field center of
circular loop of N turns is:
BN
o I
2R
I = current through the loop
R = radius of the loop
μ0 = permeability of free space
o  4 107 or1.257 106 T  m A
This formula is appropriate if the
radius of the loop is greater than it’s
thickness, but not for a solenoid.
Finding the Net Magnetic Field
A long straight wire carries a current of 8.0 A and a circular loop of
wire carries a current of 2.0 A and has a radius of 0.030 m. Find the
magnitude and direction of the magnetic field at the center of the loop.
Explain why B1 is in the upward direction and B2 is in the downward
direction.
Why is it a good first guess that B1 > B2 ?
21.7 Magnetic Fields Produced by Currents
o I1 o I 2 o  I1 I 2 
B

 
 
2 r 2R
2 r R 

4 10
B

T  m A  8.0 A
2.0 A 

  1.1105 T

2
  0.030 m 0.030 m 
7
What is the current direction in
the loop (as seen from
above) and which end is the
north pole?
A. CW – top
B. CW – bottom
C. CCW – top
D. CCW - bottom
Magnetic force on a moving charge due to
an external magnetic field
• By virtue of its motion, any moving charge is a magnet
whether positive or negative.
• In the presence of an external magnetic field, the charge
will experience a force (we ignore the tiny field due to the
charge itself.
• If the net force is non-zero, the particle will accelerate in
accordance with Newton’s 2nd Law.
• Recall that acceleration results in a change in either
speed OR direction.
The direction of the magnetic force on a
charge moving in an external B field
Right Hand Rule No. 1.
Extend the right hand so the
fingers point
along the direction of the
magnetic field and the thumb
points along
the velocity of the charge. The
palm of the hand then faces in
the
direction of the magnetic force
that acts on a positive charge.
If the moving charge is
negative, use the left hand.
The magnitude of the magnetic force on a
charge moving in an external B field
|Fm|= qvB(sinθ)
• θ is the angle between the direction of motion and the
direction of B
• B is an external field caused by magnetic objects that are
not always shown
F=0
F<Fmax
F = Fmax
Magnetic Force on a moving charge due to
an external B field
Fm = qvBsinθ
• Only a moving charge
experiences a force.
• θ is the angle between the
direction of motion and the
direction of B. There is no force
if sin θ = 0
• Therefore, there must be a
component of velocity
perpendicular to the external
field, or F = 0.
Magnetic Force on a moving charge
due to an external B field
Fm = qvBsinθ
• The force is mutually
perpendicular to v
and B.
• The force on a
negative moving
charge is shown by
the left hand rule!
Conceptual Problem
A positive charge is
traveling in the direction
shown by the arrow. It
enters the external B field
The particle experiences
a force:
a. to the right
b. to the left
c. into the page
d. out of the page

B
Out of the page
21.3 The Motion of a Charged Particle in a Magnetic Field
•The magnetic force always remains
perpendicular to the velocity.
•A constant force perpendicular to velocity
results in a centripetal acceleration and
uniform circular motion. Recall:
v2
ac 
r
•According to Newton’s Law, F = ma
For the magnetic force on a charged particle
v2
Fm  m
r
v2
qvB  m
r
21.4 The Mass Spectrometer
Chemists and biologists use the “mass spec” to identify the the
mass and/or charge of molecules.
2
v
qvB  m
r
21.4 The Mass Spectrometer
The mass spectrum of naturally
occurring neon, showing three
isotopes.
How much Deuterium in my sample?
Deuterium, (“heavy hydrogen”) has an
extra neutron in its nucleus, along
with its one proton. Researchers want
to know the percentage of deuterium
in a sample of hydrogen. The
hydrogen is stripped of its electron,
and then is accelerated through the
metal plates with a potential
difference of 2100 Volts. It then
enters a uniform B field 0.1T, out of
the page. Ignore effects due to
gravity.
At what radius should the detector be
placed to detect the deuterium?
mp = mn = 1.67 x 10-27 kg
q = e = 1.60 x 10-19 C
v = 4.5 x 105 m/s (from conservation of
energy).
How much Deuterium in my sample?
Use Newton’s Law to find an
expression for r:
v2
Fm  qvB  m
r
r = 9.4 x 10-2 m
Ranking Task
3 particles move in a
mass spectrometer
with a B field pointing
out of the page. They
have the same mass
and speed. Rank the
particles in order of
charge magnitude,
greatest to least:
v2
Fm  qvB  m
r
a. 3,2,1
b. 3,1,2
c. 2,3,1
d.1,3,2
e. 1,2,3
21.3 The Motion of a Charged Particle in a Magnetic Field
Conceptual Example 2
A Velocity Selector
A velocity selector is a
device for measuring
the velocity of a charged
particle. The device
operates by applying
electric and magnetic
forces to the particle in
such a way that these
forces balance.
How should an electric
field be applied so that
the force it applies to the
particle can balance
the magnetic force?
A.up
B.down
C.left
D.right
21.5 The Force on a Current in a Magnetic Field
The magnetic force
on the
moving charges
pushes the
wire to the right.
21.5 The Force on a Current in a Magnetic Field
The magnetic force on each moving charge
Fm  qvB sin 
 q 
Fm   
vt B sin 

t L

I
Fm  ILB sin 
Force on a wire
In New York City, the earth's magnetic field
has a vertical component of 5.2 x 10-5 T that
points downward (perpendicular to the
ground) and a horizontal component of 1.8 x
10-5 T that points toward geographic north
(parallel to the ground). What is the
magnitude and direction of the magnetic
force on a 16.0 m long, straight wire that
carries a current of 16 A perpendicularly into
the ground?
Force on a wire
In New York City, the earth's magnetic field has a
vertical component of 5.2 x 10-5 T that points
downward (perpendicular to the ground) and a
horizontal component of 1.8 x 10-5 T that points
toward geographic north (parallel to the ground).
What is the magnitude and direction of the
magnetic force on a 16.0 m long, straight wire that
carries a current of 16 A perpendicularly into the
ground?
Ans: 4.6 x 10-3 Newtons pointing east
21.6 The Torque on a Current-Carrying Coil
• The two forces on the loop have equal magnitude but an application
of RHR-1 shows that they are opposite in direction, causing the loop to
rotate.
• There is no net force, but there is a net Torque about the shaft.
• Of course we all remember torque!
  Fr sin 
21.6 The Torque on a Current-Carrying Coil
  Fr sin 
•The loop tends to rotate such that its
•normal becomes aligned with the
magnetic field.
•At this point there will no longer be a
torque.
What happens to the loop?
The magnetic field
exerts:
a. a net force and a net
torque
b. a net force but no net
torque
c. a net torque, but no
net force
d. neither a net force,
nor a net torque
What happens to this loop?
B = 0.25T, I = 12 A
Single turn square with
sides of 0.32m length
Part 1: Is there a torque?
a. yes, top out of the page,
bottom into the page
b. yes, left side out of the
page, right side into the
page
c. no torque
21.6 The Torque on a Current-Carrying Coil
Net torque    ILB 12 w sin    ILB 12 w sin    IAB sin 
magnetic
moment

  NIA B sin 
number of turns of wire
What happens to this loop?
B = 0.25T, I = 12 A
Single turn square with
sides of 0.32m length
Part 2: What is the
magnitude of the torque?
What happens to this loop?
B = 0.25T, I = 12 A
Single turn square with sides
of 0.32m length
Part 2: What is the magnitude
of the torque?
 = F(L/2)
 = NIAB
top
+ F(L/2)bottom Or
= .307 N-m
The Basics of the DC Motor
• The armature refers
to the coil of wire
(usually more than
one!) wound around
an iron core.
• The “brushes” are
conductive.
• The half-rings are
commonly called the
commutator. Their
job is to reverse the
current.
The Basics of the DC Motor-1
The magnetic
field of the
magnet exerts a
torque on the
loop (armature)
causing it to turn
clockwise . Note
the numbers on
each side of the
commutator.
Each person
should make a
sketch
2
1
The Basics of the DC Motor-2
2. Look closely at
the half-rings
and the
brushes.
Is there a force on
the loop? If so
what causes it?
If not, explain why
is the motor still
spinning? Or is it?
2
The Basics of the DC Motor -3
You draw in the
following:
• The forces on the
sides of the loops
• The direction of the
current
• The numbers on
each side of the
commutator
• The direction the
motor is turning