Download chap 21 magnetism

Chap 21 & 22: Magnets & Magnetic Fields
objectives
• Did this
– Charges
– Force between charges & Electric Field
– Moving charges, current
• will do this
– Magnetic Field
– Force on moving charges in magnetic field
– Generation of magnetic field by moving charges
– Generation of current by moving magnetic field
Examples of Magnets
•
•
•
•
•
•
•
Compass
Earth
Hi-Fi speakers
Fridge magnets
Electric motors
Scrap yards
Cupboard doors
• video/audio tapes
Properties of magnets
As with charges we find that there are
attractive and repulsive forces.
We find that magnets stick to certain
non-magnetised materials
We find that magnets can both attract
and repel each other
EARTH’S MAGNETIC FIELD
Aurora Movie
Magnetic Induction
Magnetism can be induced in materials by
rubbing with another magnetised material
Ferromagnetic materials such as iron, cobalt,
gadolinium and dysprosium can become
permanently magnetic
Paramagnetic materials such as steel
can become magnetised but this will
only last for a short time
Magnetic Induction
A permanent magnetised ferromagnet
can thus be attracted to paramagnetic
material by inducing magnetism in that
material
Magnets are Cool!
• North Pole and South Pole
– Opposites Attract
– Likes Repel
S
N
• Magnetic Field Lines
– Arrows give direction
– Density gives strength
– Looks like dipole!
Lets Break it!
-
+
Permanent Magnets
• North Pole and South Pole
– Opposites Attract
– Likes Repel
S
N
• Magnetic Field Lines
– Arrows give direction
– Density gives strength
– Looks like dipole!
Lets Break it!
S
N
S
N
Field Lines of Bar Magnet
S
Complete the lines
N
Magnetic Poles
In electrostatics there are two types of charges:
positive and negative
Similarly there are two types of “poles”:
North and South
Like poles repel
Dislike poles attract
By convention:
The North pole of a compass needle points to
the geographical north pole.
Quick Quiz
North
The Geographical North pole is defined where
the axis of rotation of the earth goes through
the arctic
Is this:
•
•
•
•
Exactly the north magnetic pole
Nearly the north magnetic pole
Exactly the south magnetic pole
Nearly the south magnetic pole
Monopoles
Unlike with electric charge no isolated magnetic
pole or monopole has ever been discovered
A north pole is always found
with a corresponding south pole
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)
Magnetic Field
Magnetic Field like the Electric Field is another
example of a vector field
It is defined everywhere
It has a magnitude
Units:
N
1
C ms
Tesla (T)
It has a direction, the direction that a compass
needle would point
Magnetic Field Lines
If we move a compass around and record the
direction it points everywhere we can map out the
direction of the magnetic field lines
Magnetic Field Lines
Magnetic Field Lines
Experiments of Pierre
de Maricourt mapped
out the field lines on
naturally magnetic
sphere
Demonstrated that
they all pointed to
two diametrically
opposed points or
“poles”.
Moving charges
in a magnetic field
Moving charges in a magnetic field
experience a magnetic force
Magnetic Field
B
S
N
Magnetic Field, B, is in direction
compass needle points
N
S
Magnitude is defined in terms
of force on moving charges
Moving charge in magnetic field
B
B
B
+
v
FB
Experiments
show
Electric 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!
Difference between
Electric
& Magnetic Forces
• acts in the direction of
the electric field
• acts on a charged
particle regardless of
whether the particle is
moving
• does work in
displacing the particle
• acts perpendicular to
the magnetic field
• acts on a charged
particle only when the
particle is moving
• does no work in
displacing the particle
Force on a moving charge
The result of all of these experiments can be summarised
by this equation
FB  qv  B
We can use this relationship to define the magnitude of B
FB  qv  B
Units:
N
C ms 1
Tesla (T)
Work & Energy
Magnetic force
does no work in
displacing a
moving particle
speed cannot change
but velocity and
direction can
Kinetic energy
of particle cannot
change
Charged particle in uniform
magnetic field
FB  qv  B
Magnetic field into board
+
+
+
FB
+
+
v
v
+
+
Note speed never
changes
but direction does
Force is always
 to v
Charged particle in uniform
magnetic field
Magnetic field into board
FB  qv  B
+
FB
+
v
Since force is always radial it
acts to keep particle moving
in a circle
2
mv
FB  qvB 
r
mv
qB 
r
mv
r
qB
Right hand rule
Review RHR
• Force on moving (+) charge
in Magnetic field
+ + + +v
F
I
– Thumb….. gives F on + charge
– fingers……. I(or v),
– palm….. B (field)
•Magnetic field produced by
moving charge.
x
–Thumb I, fingers where you
want it, palm gives B
•
Thumb out, fingers
up, palm left.
Palm out of page.
Direction of Magnet Force on
Moving Charges
Velocity
out of page
out of page
out of page
out of page
B
right
left
top
down
Force
Right Hand Rule
• Thumb ___, Fingers ___, palm ___
• Negative charge has opposite F!
Preflight
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
Force on moving charge in
magnetic Field
• The magnitude of the magnetic force FB
exerted on the particle is proportional to the
charge q and to the speed of the particle v
• The magnitude and direction of the force FB
depend on the velocity of the particle v and
the magnitude and direction of the magnetic
field B
Force on moving charge in
magnetic Field
• When the particle moves parallel to the
magnetic field vector, the magnetic force
acting on the particle is zero
• When the particle’s velocity vector v makes
an angle   0 with the magnetic field the
magnetic force acts in a direction
perpendicular to both v and B i.e. F is  to
the plane formed by v and B
Force on moving charge in
magnetic Field
• The magnetic force exerted on a positive
charge is in the opposite direction of the
force exerted on a negative charge moving
in the same direction
• The magnitude of the magnetic force
exerted on the moving particle is
proportional to sin  where  is the angle
the particles velocity vector makes with the
direction of B
Charged particle in uniform
magnetic field
mv
r
qB
velocity
rqB
v
m
Bubble chamber
p mv

 rB
q
q
angular velocity
v qB
 
r m
Mass spectrometer
m rB

q
v
Direction of Magnet Force on
Moving Charges
Velocity
out of page
out of page
out of page
out of page
B
right
left
up
down
Force
Right Hand Rule
• Thumb ___, Fingers ___, palm ___
• Negative charge has opposite F!
Preflight
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
Magnitude of Magnet Force on
Moving Charges V

• The magnetic force on a charge depends onB
the magnitude of the charge, its velocity,
and the magnetic field.
• F = q v B sin()
– Direction from RHR
• Thumb (v), fingers (B), palm (F)
– Note if v is parallel to B then F=0
Example
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) 3
4) All Same
2) The force on particle 3 is in the same direction as the force on particle 1.
B
1) True
2) False
3
2
1
Electric vs Magnetic
Source:
Act on:
Magnitude:
Direction:
Electric
Magnetic
Charges
Charges
F=Eq
Parallel E
Moving Charges
Moving Charges
F = q v B sin()
Perpendicular to v,B
Velocity Selector
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.
v
xxxxxxxxxxxx
xxxxxxxxxxxx E
xxxxxxxxxxxx
xxxxxxxxxxxx
xxxxxxxxxxxx
What do you need to change if want to select particles
with a negative charge?
Motion of q in uniform B field
• Force is perpendicular to B,v
x
x
x x x x x x
x x R
x x x x
x
x x x x x x
– B does no work! (W=F d cos  )
x x x x x x x
– Speed is constant (W=D K.E. )
x x x x x x x
– Circular motion
• Calculate R
x
x x x x x x
Uniform B into page
x x x x x x x
x
x x x x x x
Preflight
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 in chamber 2.
1) v2 < v1
2) v2 = v1
3) v2 > v1
Preflight
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
Compare the magnitude of the magnetic field in chambers 1
and 2
1) B1 > B2
2) B1 = B2.
3) B1 < B2
Solenoids
Magnitude of Field inside of solenoid : B=m0 n I
n is the number of turns of
wire/meter on solenoid.
Direction Thumb direction of I, fingers
point toward center, palm gives direction
of B.
What is the net force between the two solenoids?
a)Attractive
b) Zero
b)Repulsive
Look at field lines, opposites attract.
Look at currents, same direction attract.