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Magnetism
Mr. Burns
History
 Term comes from the ancient Greek city of
Magnesia, at which many natural magnets were
found. We now refer to these natural magnets
as lodestones (also spelled loadstone; lode means
to lead or to attract) which contain magnetite, a
natural magnetic material Fe3O4.
 Pliny the Elder (23-79 AD Roman) wrote of
a hill near the river Indus that was made
entirely of a stone that attracted iron.
History
 Chinese as early as 121 AD knew that an
iron rod which had been brought near one of
these natural magnets would acquire and
retain the magnetic property…and that such a
rod when suspended from a string would align
itself in a north-south direction.
 Use of magnets to aid in navigation can be
traced back to at least the eleventh century.
History
Basically, we knew the phenomenon existed and
we learned useful applications for it.
We did not understand it.
Finally, the Science
 Not until 1819 was a connection between electrical and
magnetic phenomena shown. Danish scientist Hans Christian
Oersted observed that a compass needle in the vicinity of a
wire carrying electrical current was deflected!
 In 1831, Michael Faraday discovered that a momentary
current existed in a circuit when the current in a nearby
circuit was started or stopped
 Shortly thereafter, he discovered that motion of a
magnet toward or away from a circuit could produce the same
effect.
History: The discovery
All magnetic
phenomena result
from forces between
electric charges in
motion.
History: More Detail
 Ampere first suggested in 1820 that
magnetic properties of matter were due to tiny
atomic currents
 All atoms exhibit magnetic effects
 Medium in which charges are moving has
profound effects on observed magnetic forces
Top Ten things we will learn about Magnetism
1. There are North Poles and South Poles.
2. Like poles repel, unlike poles attract.
3. Magnetic forces attract only magnetic materials.
4. Magnetic forces act at a distance.
5. While magnetized, temporary magnets act like permanent magnets.
6. A coil of wire with an electric current flowing through it becomes a magnet.
7. Putting iron inside a current-carrying coil increases the strength of the
electromagnet.
8. A changing magnetic field induces an electric current in a conductor.
9. A charged particle experiences no magnetic force when moving parallel to a
magnetic field, but when it is moving perpendicular to the field it experiences a force
perpendicular to both the field and the direction of motion.
10. A current-carrying wire in a perpendicular magnetic field experiences a force in a
direction perpendicular to both the wire and the field.
Magnetic Poles
Every magnet has at least one north pole and one south pole. By
convention, we say that the magnetic field lines leave the North end
of a magnet and enter the South end of a magnet.
 North Pole and South Pole
 Opposites Attract
 Likes Repel
-
+
 Magnetic Field Lines
 Arrows give direction
 Density gives strength
 Looks like dipole!
S
N
Let’s Break It
If you take a bar magnet and break it into two pieces, each piece will again have a North
pole and a South pole.
If you take one of those pieces and break it into two, each of the smaller pieces will have
a North pole and a South pole.
No matter how small the pieces of the magnet become, Each piece will have a North pole
and a South pole
S
N
S
N S
N
No Monopoles Allowed
It has not been shown to be possible to end up with a single
North pole or a single South pole, which is a monopole ("mono"
means one or single, thus one pole).
S
N
Note: Some theorists believe that magnetic monopoles may
have been made in the early Universe. So far, none have been
detected.
Field Lines of Bar Magnets
S
N
Magnetic field lines don’t start or stop.
There are no magnetic charges (monopoles)
The Concept of “Fields”
Michael Faraday
realized that ...
A magnet has a
‘magnetic field’
distributed throughout
the surrounding space
Magnetic Field Lines
Magnetic field lines describe the structure of magnetic fields
in three dimensions. They are defined as follows. If at any
point on such a line we place an ideal compass needle, free to
turn in any direction (unlike the usual compass needle, which
stays horizontal) then the needle will always point along the
field line.
Field lines converge where the magnetic force is strong, and
spread out where it is weak. For instance, in a compact bar
magnet or "dipole," field lines spread out from one pole and
converge towards the other, and of course, the magnetic
force is strongest near the poles where they come together.
Field Lines Around a Magnet
Field Lines Around a Magnet Sphere
Field Lines Around a Magnet Sphere like the Earth
Action at a Distance Explained
Although two magnets
may not be touching,
they still interact
through their
magnetic fields.
This explains the
‘action at a distance’,
say of a compass.
Act 1
Preflight 8.1
1
Which drawing shows the correct
field lines for a bar magnet?
(1)
(2)
S
N
S
N
S
N
2
(3)
3
Act 1
Preflight 8.1
1
Which drawing shows the correct
field lines for a bar magnet?
(1)
(2)
S
N
S
N
S
N
2
(3)
• Magnetic field lines are continuous
• Arrows go from N to S outside the
magnet (S to N inside).
3
Comparison: Electric Field Lines vs. Magnetic Field Lines
 Similarities
 Density gives strength
 Arrow gives direction
 Leave +, North
 Enter -, South
 Differences
 Start/Stop on electric charge
 No Magnetic Charge, lines are continuous!
 FYI (notation)
 x x x x x x x INTO Page
 • • • • • • • • • OUT of Page
No Magnetic Charges


Magnetic Fields are created by
moving electric charge!
Where is the moving charge?
Orbits of electrons about nuclei
Intrinsic “spin” of
electrons (more
important effect)
Magnets Have Magnetic Fields
We will say that a moving charge sets up in the space
around it a magnetic field,
and
it is the magnetic field which exerts a force on any other
charge moving through it.
Magnetic fields are vector
quantities….that is, they have a
magnitude and a direction!
Defining Magnetic Field Direction
Magnetic Field vectors as written as B
Direction of magnetic field at any point is defined
as the direction of motion of a charged particle on
which the magnetic field would not exert a force.
Magnitude of the B-vector is proportional to the
force acting on the moving charge, magnitude of the
moving charge, the magnitude of its velocity, and the
angle between v and the B-field. Unit is the Tesla or
the Gauss (1 T = 10,000 G).
Relationship Between Force, Magnetic field direction, and Current Flow
Flow of Positive Charges
F  qv  B
Force on Conductor
Magnetic Field
Right Hand Rule
B
F
v
If the right thumb points in the direction
of the current (flow of positive charge), and
the extended fingers point in the direction
of the magnetic field, the force is in the
direction in which the right palm pushes.
Negative charge has opposite F!
Direction of Magnetic Force on Moving Charges
Right Hand Rule
Velocity
out of screen
B
right
Force
UP
B
F  qv  B

Thumb v , Fingers B , Palm F
F
v
Direction of Magnetic Force on Moving Charges
Right Hand Rule
Velocity
B
out of screen
right
out of screen
left
Force
UP
DOWN
B
F  qv  B

Thumb v , Fingers B , Palm F
F
v
Direction of Magnetic Force on Moving Charges
Right Hand Rule
Velocity
B
Force
out of screen
right
out of screen
left
DOWN
out of screen
up
LEFT
UP
B
F  qv  B

Thumb v , Fingers B , Palm F
F
v
Direction of Magnetic Force on Moving Charges
Right Hand Rule
Velocity
B
Force
out of screen
right
out of screen
left
DOWN
out of screen
up
LEFT
out of screen
down
RIGHT
UP
B
F  qv  B

Thumb v , Fingers B , Palm F
F
v
Act 2
Each chamber has a unique magnetic
field. A positively charged particle
enters chamber 1 with velocity 75 m/s
up, and follows the dashed trajectory.
2
1
v = 75 m/s
q = +25 mC
What is the direction of the force on the particle just as it enters
region 1?
1) up
2) down
3) left
4) right
5) into page
6) out of page
Act 2
Each chamber has a unique magnetic
field. A positively charged particle
enters chamber 1 with velocity 75 m/s
up, and follows the dashed trajectory.
2
1
v = 75 m/s
q = +25 mC
What is the direction of the force on the particle just as it enters
region 1?
1) up
Particle is moving straight upwards
2) down
then veers to the right.
3) left
4) right
5) into page
6) out of page
Act 2
Each chamber has a unique magnetic
field. A positively charged particle
enters chamber 1 with velocity 75 m/s
up, and follows the dashed trajectory.
2
1
v = 75 m/s
q = +25 mC
What is the direction of the magnetic field in region 1?
1) up
2) down
3) left
4) right
5) into page
6) out of page
Act 2
Each chamber has a unique magnetic
field. A positively charged particle
enters chamber 1 with velocity 75 m/s
up, and follows the dashed trajectory.
2
1
v = 75 m/s
q = +25 mC
What is the direction of the magnetic field in region 1?
1) up
_
2) down
v (thumb) points up, F(palm) points
3) left
right: so B(fingers) must point out.
4) right
_
5) into page
6) out of page
ACT: 2 Chambers
Each chamber has a unique magnetic
field. A positively charged particle
enters chamber 1 with velocity 75 m/s
up, and follows the dashed trajectory.
2
1
v = 75 m/s
q = +25 mC
What is the direction of the magnetic field in region 2?
1) up
2) down
3) left
4) right
5) into page
6) out of page
Act 3
Each chamber has a unique magnetic
field. A positively charged particle
enters chamber 1 with velocity 75 m/s
up, and follows the dashed trajectory.
2
1
v = 75 m/s
q = +25 mC
What is the direction of the magnetic field in region 2?
1) up
2) down
v (thumb) points right, F(palm) points
3) left
up, B(fingers) point in.
4) right
5) into page
6) out of page
Magnitude of Magnetic Force on Moving Charges with Angles

The magnetic force on a charge depends
on the magnitude of the charge, its
velocity, and the magnetic field.
F = q v B sin(q)

Direction from RHR


Thumb (v), fingers (B), palm (F)
Note if v is parallel to B then F = 0
V
q
B
Act 3: Moving Charges
The three charges below have equal charge and speed, but are
traveling in different directions in a uniform magnetic field.
1) Which particle experiences the greatest magnetic force?
1) 1
2) 2
) 3 4) All Same
F = q v B sin(q)
2) The force on particle 3 is in the same direction as the force on
particle 1.
B
1) True
2) False
Thumb (v), fingers (B), palm (F)
into page!
3
2
1
Comparison: Electric vs. Magnetic Force
Electric
Magnetic
Source:
Charges
Moving Charges
Act on:
Charges
Moving Charges
Magnitude:
F = qE
F = q v B sin(q)
Direction:
Parallel to E
Perpendicular to v,B
Act Practice
Three points are arranged in a uniform
magnetic field. The B field points into
the screen.
  
Magnetic Force: F  qv  B
1) A positively charged particle is located at point A and is stationary.
The direction of the magnetic force on the particle is:
a) right
b) left
d) out of the screen
c) into the screen
e) zero
If v = 0  F = 0.
2) The positive charge moves from point A toward B. The direction of


the magnetic force on the particle is:
If v  B then F = qvB
a) right
b) left
d) out of the screen
c) into the screen
e) zero
Act Practice

Two protons each move at speed v (as shown in
the diagram) in a region of space which
contains a constant B field in the -z-direction.
Ignore the interaction between the two
protons.
y
1
v
B
2
v
z
x
1) What is the relation between the magnitudes of the forces on the two protons?
(a) F1 < F2
(b) F1 = F2
(c) F1 > F2
2) What is F2x, the x-component of the force on the second proton?
(a) F2x < 0
(b) F2x = 0
(c) F2x > 0
3) Inside the B field, the speed of each proton:
(a) decreases
(b) increases
(c) stays the same
Act Practice

Two independent protons each move at
speed v (as shown in the diagram) in a
region of space which contains a
constant B field in the -z-direction. Ignore
the interaction between the two protons.
y
1
v
B
2
v
z
x
What is the relation between the magnitudes of the forces on the two protons?
(a) F1 < F2
(b) F1 = F2
(c) F1 > F2
• The magnetic force is given by:



F  q v  B  F  qvB sin θ
• In both cases the angle between v and B is 90!!
Therefore F1 = F2.
Act Practice

F1
Two independent protons each move at
speed v (as shown in the diagram) in a
region of space which contains a
constant B field in the -z-direction. Ignore
the interaction between the two protons.
F2
y
1
v
B
2
v
z
x
What is F2x, the x-component of the force on the second proton?
(a) F2x < 0
(b) F2x = 0
(c) F2x > 0
• To determine the direction of the force, we use the
right-hand rule.

 
F  qv  B
• As shown in the diagram, F2x < 0.
Act Practice

Two protons each move at speed v (as
shown in the diagram) in a region of
space which contains a constant B field in
the -z-direction. Ignore the interaction
between the two protons.
y
1
v
B
2
z
v
x
Inside the B field, the speed of each proton:
(a) decreases
(b) increases
(c) stays the same
Although the proton does experience a force
(which deflects it), this is always  to v .
Therefore, there is no possibility to do work, so
kinetic energy is constant and v is constant.
Act 3
Determine magnitude and direction of
magnetic field such that a positively
charged particle with initial velocity
v travels straight through and exits
the other side.
FB
E
v
FE
Electric force is down, so need magnetic force up.
By RHR, B must be into page
For straight line, need |FE |= |FB |
q E= q v B sin(90)
B = E/v
What direction should B point if you want to select
negative charges? FE would be up so FB must be down.
1) Into Page
2) Out of page
3) Left
4) Right
Motion of Charge Q in a Uniform Field B
Force is perpendicular to B,v



B does no work! (W=F d cos q )
Speed is constant (W=D K.E. )
Circular motion
Solve for R:
v2
F m
R
v2
qvBsin(q )  m
R
x
x
x x x x x x
x x R
x x x x
x
x x x x x x
x
x x x x x x
x
x x x x x x
F
v
v

F

x x x x x x x
Uniform B into page
mv
R
qB
Act 4
Each chamber has a unique magnetic
field. A positively charged particle
enters chamber 1 with velocity v1= 75
m/s up, and follows the dashed
trajectory.
2
1
v = 75 m/s
q = +25 mC
What is the speed of the particle when it leaves chamber 2?
1) v2 < v1
2) v2 = v1
3) v2 > v1
Magnetic force is always
perpendicular to velocity, so it
changes direction, not speed of
particle.
Act 5
Each chamber has a unique magnetic
field. A positively charged particle
enters chamber 1 with velocity v1= 75
m/s up, and follows the dashed
trajectory.
2
1
v = 75 m/s
q = +25 mC
Compare the magnitude of the magnetic field in chambers 1 and 2
1) B1 > B2
2) B1 = B2.
R
mv
qB
3) B1 < B2
Larger B, greater force, smaller R
Preflight 8.9
Each chamber has a unique magnetic
field. A positively charged particle enters
chamber 1 with velocity v1= 75 m/s up,
and follows the dashed trajectory.
2
1
v = 75 m/s
q = ?? mC
A second particle with mass 2m enters the chamber and follows
the same path as the particle with mass m and charge q=25
mC. What is its charge?
1) Q = 12.5 mC
2) Q = 25 mC
3) Q = 50 mC
Act 6
Each chamber has a unique magnetic
field. A positively charged particle
enters chamber 1 with velocity v1= 75
m/s up, and follows the dashed
trajectory.
2
1
v = 75 m/s
q = ?? mC
A second particle with mass 2m enters the chamber and follows the
same path as the particle with mass m and charge q=25 mC. What is its
charge?
1) Q = 12.5 mC
2) Q = 25 mC
3) Q = 50 mC
mv
R
qB
Since m is doubled and the path is the same, therefore
q also has to double
Magnetic Force on a Current Carrying
Conductor

A force is exerted on a current-carrying wire
placed in a magnetic field


The current is a collection of many charged
particles in motion
The direction of the force is given by the
Right Hand Rule.
Force on a Wire

The blue x’s indicate the
magnetic field is directed
into the page


Blue dots would be used to
represent the field directed
out of the page


The x represents the tail of the
arrow
The • represents the head of
the arrow
In this case, there is no
current, so there is no force
Force on a Wire



B is into the page
The current is up the page
The force is to the left
Force on a Wire



B is into the page
The current is down the page
The force is to the right
Force on a Wire, equation



The magnetic force is exerted on each moving charge in the wire
The total force is the sum of all the magnetic forces on all the
individual charges producing the current
F = B I ℓ sin θ
 θ is the angle between B and the direction of current I
 The direction is found by the Right hand.
Where did this
Force on a wire
formula come
from?
F  qvB sin q 
For n electrons through a volume of wire
F   nAL  qvB  sin q 
  nqvA LB  sin q 
  I  LB  sin q 
 ILB sin q 
Example

A 30 m long wire carries a current of 10 A in
a 1 T magnetic field.
Find the maximum magnetic force on the
wire.
F  IlB sin q 
 10 A  30m 1T  sin  90 
 300 N
Act 7
A rectangular loop of wire is carrying current as shown. There
is a uniform magnetic field parallel to the sides A-B and C-D.
C
D
B
A
I
B
What is the direction of the force on section A-B of the wire?
force is zero
out of the page
into the page
What is the direction of the force on section B-C of the wire?
force is zero
out of the page
into the page
Act 7
A rectangular loop of wire is carrying current as shown. There
is a uniform magnetic field parallel to the sides A-B and C-D.
B
C
D
q
B
A
I
B
I
F=ILBsinq
Here q = 0.
What is the direction of the force on section A-B of the wire?
force is zero
out of the page
into the page
Act 7
A rectangular loop of wire is carrying current as shown. There
is a uniform magnetic field parallel to the sides A-B and C-D.
I
C
D
F
X
A
I
B
B
Palm into page.
What is the direction of the force on section B-C of the wire?
force is zero
out of the page
into the page
Torque on Current Loop in B Field
C
D
•
F
F
X
B
A
I
F
A
B
C
D
B
F
The loop will Spin in place
Look from here
Currents Create B Fields
Magnitude of B a distance r from (straight) wire:
0I
B
2r
B
0  4   10 7 Tm / A
µo is called the permeability of free space
r = distance from wire
Right-Hand Rule, part deux!
Thumb:
Fingers:
r
•
Here’s a
current-carrying
wire.
Current I OUT
of page.
Lines of B
along wire in direction of current
curl along direction of Field lines
Right Hand rule Part 2
Fingers give B!
Act 8
A long straight wire is carrying current from left to
right. Near the wire is a charge q with velocity v
v
v
•
(a)
F
r
B•
(b)
r
• F
I
Compare magnetic force on q in (a) vs. (b)
a) has the larger force
b) has the larger force
c) force is the same for (a) and (b)
0I
same B 
2r
same F  qvB sin q
θ is angle between v and B
(θ = 90° in both cases)
ACT: Adding Magnetic Fields
Two long wires carry opposite current
x
x
What is the direction of the magnetic field above, and midway
between the two wires carrying current – at the point marked “X”?
1) Left 2) Right
3) Up
4) Down 5) Zero
Act 9
Two long wires carry opposite current
B
x
x
What is the direction of the magnetic field above, and midway
between the two wires carrying current – at the point marked “X”?
1) Left 2) Right
3) Up
4) Down 5) Zero
Force Between Current Carrying Wires
F  I1 LB2 sin q 
 I1 LB2
I towards us
B
•
•
F
Another I towards us
u0 I 2
 I1 L
2 r
F u0 I1 I 2

L
2 d
Conclusion: Currents in same direction attract!
The force per unit length is:
I towards
us
•
d
F 0 I1I 2

l
2 d
B
 F
Another I away from us
Conclusion: Currents in opposite direction repel!
Note: this is different from the Coulomb force between like or unlike charges.
Comparison
Electric Field vs. Magnetic Field
Electric
Magnetic
Source
Charges
Moving Charges
Acts on
Charges
Moving Charges
Force
F = Eq
F = q v B sin(q)
Direction
Parallel E
Perpendicular to v,B
Charges Attract
Currents Repel
Field Lines
Opposites
Magnetic Field of a Current Loop


The strength of a
magnetic field produced
by a wire can be
enhanced by forming
the wire into a loop
All the segments, Δx,
contribute to the field,
increasing its strength
Magnetic Field of a Current Loop
Magnetic Field of a Solenoid


If a long straight wire is
bent into a coil of
several closely spaced
loops, the resulting
device is called a
solenoid
It is also known as an
electromagnet since it
acts like a magnet only
when it carries a current
Magnetic Field of a Solenoid

The field lines inside the solenoid are nearly
parallel, uniformly spaced, and close together


This indicates that the field inside the solenoid is
nearly uniform and strong
The exterior field is nonuniform, much
weaker, and in the opposite direction to the
field inside the solenoid
Magnetic Field in a Solenoid

The field lines of the solenoid resemble those
of a bar magnet
B fields Inside Solenoids
Magnitude of Field anywhere inside of solenoid:
n is the number of turns of wire/meter
on solenoid.
B=0 n I
L
0 = 4 x10-7 T m /A
(Note: N is the total number of turns counted, so n = N / L)
(Note: L is the length of the solenoid.)
Right-Hand Rule gives Direction:
Thumb - along I
B
0 NI
L
Fingers – curl into interior of solenoid
Palm – gives B
Magnetic field lines look like bar magnet! Solenoid has N and S poles!
Act 10: B fields inside Solenoids
What is the direction of the magnetic field produced
by these solenoids?
(1) to the Right
(2) to the Left
What is the net force between the two solenoids?
(1) Attractive
(2) Zero
(3) Repulsive
Act 10: B fields inside Solenoids
What is the direction of the magnetic field produced
by these solenoids?
(1) to the Right
(2) to the Left
Right Hand Rule!
Act 10: B fields inside Solenoids
What is the net force between the two solenoids?
(1) Attractive
(2) Zero
(3) Repulsive
Look at field lines, opposites attract.
Look at currents, same direction attract.
The Hall Effect



Which charges carry current?

Positive charges moving
counterclockwise experience
upward force
Upper plate at higher potential 
Negative charges moving
clockwise experience upward
force
Upper plate at lower potential
• This type of experiment led to the discovery (E. Hall, 1879) that current in
conductors is carried by negative charges (not always so in semiconductors).
Summary of Equations
Magnetic Force: FM  qvB sin q 
7
u0= 4 10
T m
A
Ampere’s Law: B 
0 I
2 r
r is the distance
from wire
Solenoid:
B
0 NI
Length of
solenoid
L
N is number of
turns
Direction via Right Hand
Rule
Current
Summary of Equations
B is magnetic
Field Strength
in Tesla
Force of a Conductor: Fwire  IlB sin q 
Θ is the angle between the
current and magnetic field
I is the current
Force on
wire
Two wires:
L is the length
of wire is m
F 0 I1I 2

l
2 d
Length of
wire
Distance
between wires
Flash: Electromagnetism
Flash: Magnetic Force on a Wire
Flash: Magnetic Field on Wire