This Week

1
This Week
Last Week
Magnetic Fields and Forces Production of Magnetic
fields by electric currents permanent magnets
We know that electricity can affect (i.e.
produce) magnetism. So, can Magnetism affect
electricity? Magnetic Force and Field Magnetic
Forces on Charged objects Currents Magnetic
Torques on current Loops
Chapter 22 Sections 1, 2 (first two pages), 9,
and 10
Amperes Law
Chapter 22 Sections 1 6, 8
2
A magnetic field does not effect a stationary
electric charge
Experimental Facts
BUT
A magnetic field does exert a force on a moving
electric charge
Detailed measurements show the magnetic force on
an electric charge
1. Proportional to speed of charge.
2. Proportional to Magnetic Field.
3. Perpendicular to Magnetic Field.
4. Perpendicular to direction of motion of
charge.
5. Direction depends on sign of charge.
6. Direction depends on direction of magnetic
field
3
A magnetic field does not effect a stationary
electric charge
Mathematically
BUT
A magnetic field does exert a force on a moving
electric charge
Multiply B by the component of v perpendicular to
B
OR
Multiply v by the component of B perpendicular to
v
Detailed measurements show the magnetic force on
an electric charge
The result is a vector perpendicular to both v
and B
1. Proportional to speed of charge.
2. Proportional to Magnetic Field.
3. Perpendicular to Magnetic Field.
Direction by right hand rule
4. Perpendicular to direction of motion of
charge.
Wrap fingers from v to B through the smallest
angle
5. Direction depends on sign of charge.
Thumb points in the vector direction
6. Direction depends on direction of magnetic
field
4
Mathematically
B
Force is out of the screen if charge is positive
v
Multiply B by the component of v perpendicular to
B
Force is into the screen, if charge is positive
OR
Multiply v by the component of B perpendicular to
v
The result is a vector perpendicular to both v
and B
Direction by right hand rule
Wrap fingers from v to B through the smallest
angle
Thumb points in the vector direction
http//www.physics.brocku.ca/faculty/sternin/120/s
lides/rh-rule.html
5
Units
B
Force is out of the screen if charge is positive
v
Newtons Coulombs meters/sec B
kg m/s2 C m/s B
Force is into the screen, if charge is positive
1 T 104 Gauss 104 G
http//www.physics.brocku.ca/faculty/sternin/120/s
lides/rh-rule.html
6
Lecture Question What is the direction of the
magnetic force?

• Into the page
• Out of the page
• Up
• Down
• Left
• Right
• Zero (No direction)

7
Lecture Question What is the direction of the
magnetic force?

• Into the page
• Out of the page
• Up
• Down
• Left
• Right
• Zero (No direction)

8
Lecture Question What is the direction of the
magnetic force?

• Into the page
• Out of the page
• Up
• Down
• Left
• Right
• Zero (No direction)

9
Lecture Question What is the direction of the
magnetic force?

• Into the page
• Out of the page
• Up
• Down
• Left
• Right
• Zero (No direction)

10
Units
Interesting result We know that the magnetic
force is the is always perpendicular to the
motion (i.e. velocity and thus displacement).
For charges that are free (not bound in a
material) we can conclude that the magnetic force
can do no work on the charge. Why? Lets go
back to the definition of work
Newtons Coulombs meters/sec B
kg m/s2 C m/s B
1 T 104 Gauss 104 G
Where the angle is the angle between Force and
Displacement. For the magnetic force, that angle
is 90o
11
Interesting result We know that the magnetic
force is the is always perpendicular to the
motion (i.e. velocity and thus displacement).
For charges that are free (not bound in a
material) we can conclude that the magnetic force
can do no work on the charge. Why? Lets go
back to the definition of work
If the magnetic force does no work, then there
can be no change in the KE (thats the W-KE
theorem). If there is no change in the KE, then
the objects speed wont change (but its velocity
will)
If the magnetic force does no work, there is no
reason to define a PE.
Where the angle is the angle between Force and
Displacement. For the magnetic force, that angle
is 90o
12
What is the trajectory of a particle with a force
on it that is always perpendicular to its
velocity and the speed doesnt change?
If the magnetic force does no work, then there
can be no change in the KE (thats the W-KE
theorem). If there is no change in the KE, then
the objects speed wont change (but its velocity
will)
q
B into screen
If the magnetic force does no work, there is no
reason to define a PE.
A charged particle in a uniform magnetic field
with velocity perpendicular to magnetic field
Uniform Circular Motion
13
You are using a mass spectrometer to determine
the composition of a protein present in bone
cancer. In this device, the sample is vaporized
and its parts are electrically charged. The ions
are accelerated through an electric potential
difference that you control by your power supply.
The ions then enter a region of constant
magnetic field through a small hole. The field
is perpendicular to the ions path. In the
magnetic field, the ion trajectory finally goes
backwards where it is detected. You then measure
the distance from where the ion enters the
magnetic field to where it is detected. Protons
(hydrogen ions) are used to calibrate the device.
If another ion with the same charge as a proton
is detected 1.4 times further away, what is the
ratio of that ions mass to the mass of the
proton? You will look up the charge and mass of
the proton later.
What is the trajectory of a particle with a force
on it that is always perpendicular to its
velocity and the speed doesnt change?
v
q
F
B into screen
A charged particle in a uniform magnetic field
with velocity perpendicular to magnetic field
Uniform Circular Motion
14
You are using a mass spectrometer to determine
the composition of a protein present in bone
cancer. In this device, the sample is vaporized
and its parts are electrically charged ions. The
ions are accelerated through an electric
potential difference that you control by your
power supply. The ions then enter a region of
constant magnetic field through a small hole.
The field is perpendicular to the ions path. In
the magnetic field, the ion trajectory finally
goes backwards where it is detected. You then
measure the distance from where the ion enters
the magnetic field to where it is detected.
Protons (hydrogen ions) are used to calibrate the
device. If another ion with the same charge as a
proton is detected 1.4 times further away, what
is the ratio of that ions mass to the mass of
the proton? You will look up the charge and mass
of the proton later.
B direction?
-
DV


Di 1.4 Dp
qi qp
Dp 2rp
Di 2ri
What is mion/mproton ?
Approach
Use magnetic force to get mass
Force on charged particle is perpendicular to its
velocity
Circular motion
No energy input by magnetic field
Speed does not change
Use potential difference to get speed
Conservation of energy
15
B direction?
Two important times in the motion
Before reaching magnetic field
Ion speed increases
Caused by potential difference
Use Conservation of Energy
DEsystem DEtransfer
Ef Eo Einput - Eoutput
Dp 2rp
Di 1.4 Dp
qi qp
choose system ion electric field
Di 2ri
What is mion/mproton ?
DEsystem DKE DPE
Approach
DEtransfer 0
Use magnetic force to get mass
Force on charged particle is perpendicular to its
velocity
Circular motion
assume vo 0
No energy input by magnetic field
DPE -q DV
Speed does not change
Use potential difference to get speed
Conservation of energy
16
Two important times in the motion
B is out
Before reaching magnetic field
Ion speed increases
Caused by potential difference
Use Conservation of Energy
DEsystem DEtransfer
Ef Eo Einput - Eoutput
For the proton
choose system ion electric field
DEsystem DKE DPE
For the ion
DEtransfer 0
assume vo 0
DPE -q DV
17
Electrospray-Ion Trap Mass Spectrometry
18
Electrospray-Ion Trap Mass Spectrometry
19
Balancing Forces
Can you balance an electric force on an object
with a magnetic force so the object is in
equilibrium?
For the object to be in equilibrium the magnetic
force on the object must be
What is required of the object?
The object needs to be charged.
The object needs to be moving.

• in the x direction
• in the y direction
• in the z direction
• in the - x direction
• in the - y direction
• in the - z direction
• 0
• it cant be in equilibrium since it is moving

What is required of space?
Electric field
In direction of force.
Magnetic field
Perpendicular to force.
20
free body diagram
To get a force in the x direction, the magnetic
field must be
For the object to be in equilibrium the magnetic
force on the object must be

• in the x direction
• in the y direction
• in the z direction
• in the - x direction
• in the - y direction
• in the - z direction
• 0
• no magnetic field can give a force in the x
  direction

• in the x direction
• in the y direction
• in the z direction
• in the - x direction
• in the - y direction
• in the - z direction
• 0
• it cant be in equilibrium since it is moving

21
To get a force in the x direction, the magnetic
field must be
z is out

• in the x direction
• in the y direction
• in the z direction
• in the - x direction
• in the - y direction
• in the - z direction
• 0
• no magnetic field can give a force in the x
  direction

22
Lecture Question To get this charged particle
to be in equilibrium, the magnetic field must be
in which direction?
z is out

• in the x direction
• in the y direction
• in the z direction
• in the - x direction
• in the - y direction
• in the - z direction
• 0
• no magnetic field can achieve equilibrium for
  this situation

23
Since a magnetic field causes a force on a moving
charged object,
For the whole wire
Add the forces on each charged object
expect it to cause a force on a wire with current
B is in
dL
Force on the single charged object
If the magnetic field is constant along the wire
L is in the direction of the current
If the magnetic field is perpendicular to the wire
24
Lecture Question A power line carries a current
of 1000 Amps from East to West. The Earths
Magnetic field, 0.0002 T, points upward at an
angle of 60o from the horizontal toward the
north. What is the magnitude of the magnetic
force on a 10 m length of current?

• 2.0 Newtons
• 1.7 Newtons
• 1 Newton
• 0 Newtons

B
60o
I
25
For the whole wire
A magnetic force on an electric current has
practical applications
Add the forces on each charged object
In the lab you use it to measure the magnetic
field with a Hall probe.
Qualitatively how does a Hall probe work?
B out
If the magnetic field is constant along the wire
A charge carrier moving in the direction of the
current has a force on it caused by the magnetic
field
If the magnetic field is perpendicular to the wire
One side of the conductor gets a charge and the
other a - charge
Charge separation produces a voltage
26
A magnetic force on an electric current has
practical applications
A more common application, the electric motor
In the lab you use it to measure the magnetic
field with a Hall probe.
Loop of wire with an electric current in a
uniform magnetic field
Loop starts in y-z plane
Qualitatively how does a Hall probe work?
B in z direction
B out
I
A charge carrier moving in the direction of the
current has a force on it caused by the magnetic
field
a
b
c
d
Side a (I is perpendicular to B)
One side of the conductor gets a charge and the
other a - charge
is in
Charge separation produces a voltage
Force is into the screen (-x)
27
A more common application, the electric motor
Side b (I is parallel to B)
Loop of wire with an electric current in a
uniform magnetic field
Force is 0
Loop starts in y-z plane
Side c (I is perpendicular to B)
B in z direction
N
I
Force is out of screen (x)
a
b
c
d
I
Side d (I is parallel to B)
S
Force is 0
Side a (I is perpendicular to B)
Entire loop
Torque
is in
Force is into the screen (-x)
28
Side b (I is parallel to B)
Force is 0
top wire
Side c (I is perpendicular to B)
Torque in the -y direction
bottom wire
Force is out of screen (x)
Torque in the -y direction
Side d (I is parallel to B)
Sum of torques in the y direction
Force is 0
t 2 r I L B
Entire loop
If the loop had many wraps of wire (N), you would
add the force on each wire to get the force on
the loop
Torque
t 2 Nr I L B
29
top wire
Area of loop 2r L A
t I BA
Torque in the -y direction
in the y direction
bottom wire
When loop is in y-z plane
B is in the z direction
Current is clockwise
Torque in the -y direction
Sum of torques in the y direction
t 2 r I L B
If the loop had many wraps of wire (N), you would
add the force on each wire to get the force on
the loop
t 2 Nr I L B
30
When loop is flat (in x-y plane).
L
N
2r
d
a
c
Area of loop 2r L A
b
I
t I BA
S
in the y direction
Side a (I is perpendicular to B)
When loop is in y-z plane
B is in the z direction
The direction of the force on wire a is
Current is clockwise

• x
• y
• z
• -x
• -y
• -z
• 0

31
The direction of the force on wire a is

• x direction
• y direction
• z direction
• - x direction
• - y direction
• - z direction
• 0

32
(No Transcript)
33
Need to reverse the current in the coil when the
coil reaches the zero torque position
To get a stronger magnetic field, iron (or
another magnetic material) is inserted in the
coil of wire.
www.scienceclarified.com
The split conductor connecting to the battery
causes the current in the top wire to always be
in the same direction
www.answers.com
The magnet field from the coil aligns the
magnetic dipoles in the iron to give a stronger
field.
34
Now, lets combine the ideas of (A) magnetic
production and (B) magnetic force
Why is there a force at all?
Well, label one current 1 and other current 2 to
make the explanation clearer
Two parallel wires have current going to the
right.
I1
I
I
I2

• The wires attract.
• The wires repel.
• One wire is attracted and the other repelled
• There is no force on either wire caused by the
  other wire

There is only a force on current 2 if there is a
magnetic field
Whats creating the other field? Answer
Current 1. To find the direction of the force, we
need direction of B
35
Why is there a force at all?
Well, label one current 1 and other current 2 to
make the explanation clearer
Find B1
I1
I1
x
B1
I2
I2
Find F
There is only a force on current 2 if there is a
magnetic field
I1
F
x
B1
I2
Whats creating the other field? Answer
Current 1. To find the direction of the force, we
need direction of B
36
Lecture Question What is the direction of the
force that current 2 exerts on current 1?
I1
I2

• Into the Page
• Out of the page
• Up
• Down
• Left
• Right
• There is no force

37
Lecture Question Two parallel wires have current
going to the left.
I
I

• The wires attract.
• The wires repel.
• One wire is attracted and the other repelled
• The electric attraction cancels the magnetic
  repulsion
• The electric repulsion cancels the magnetic
  attraction
• There is no force on either wire caused by the
  other wire