Using the

1
Using the Clicker

• If you have a clicker now, and did not do this
  last time, please enter your ID in your clicker.
• First, turn on your clicker by sliding the power
  switch, on the left, up. Next, store your student
  number in the clicker. You only have to do this
  once.
• Press the button to enter the setup menu.
• Press the up arrow button to get to ID
• Press the big green arrow key
• Press the T button, then the up arrow to get a U
• Enter the rest of your BU ID.
• Press the big green arrow key.

2
Magnetic flux

• Magnetic flux is

3
Magnetic flux

• Magnetic flux is a measure of the number of
  magnetic field lines passing through something,
  such as a loop. If we define the area of the loop
  as a vector, with its direction perpendicular to
  the plane of the loop, the magnetic flux is given
  by
• where ? is the angle between the magnetic field
  and the area vector.
• The unit of magnetic flux is the weber. 1 Wb 1
  T m2.

4
Magnetic flux

• The more field lines pass through an area, the
  larger the flux.
• Lots of flux. No flux.
• Some flux.

5
Magnetic flux from a bar magnet

• A bar magnet passes from right to left through a
  loop of wire. Flux is positive when the field
  lines pass one way through the loop, and negative
  when they go in the opposite direction. What, if
  anything, is wrong with the graph of magnetic
  flux for this situation?
• There's nothing wrong
• with it.
• 2. There is something
• wrong with it (you
• specify what it is)

6
Observations with a magnet, coil, and galvanometer

• Lets make a few observations, using a magnet
  near a coil connected to a galvanometer (a
  sensitive current meter). The magnets north pole
  points at the coil.

Situation Predict what the galvanometer needle does. What the needle actually does.
The magnet is moved toward the coil. No basis for prediction.
The magnet is moved away from the coil.
The magnet is moved toward the coil again, but more slowly.
The magnet is held at rest near the coil.
The magnet is held at rest and the coil is moved toward the magnet.
7
Observations with a magnet, coil, and galvanometer

• Lets make a few observations, using a magnet
  near a coil connected to a galvanometer (a
  sensitive current meter). The magnets north pole
  points at the coil.

Situation Predict what the galvanometer needle does. What the needle actually does.
The magnet is moved toward the coil. No basis for prediction. Needle deflects to the left.
The magnet is moved away from the coil.
The magnet is moved toward the coil again, but more slowly.
The magnet is held at rest near the coil.
The magnet is held at rest and the coil is moved toward the magnet.
8
Observations with a magnet, coil, and galvanometer

• Lets make a few observations, using a magnet
  near a coil connected to a galvanometer (a
  sensitive current meter). The magnets north pole
  points at the coil.

Situation Predict what the galvanometer needle does. What the needle actually does.
The magnet is moved toward the coil. No basis for prediction. Needle deflects to the left.
The magnet is moved away from the coil. Opposite to the above.
The magnet is moved toward the coil again, but more slowly.
The magnet is held at rest near the coil.
The magnet is held at rest and the coil is moved toward the magnet.
9
Observations with a magnet, coil, and galvanometer

• Lets make a few observations, using a magnet
  near a coil connected to a galvanometer (a
  sensitive current meter). The magnets north pole
  points at the coil.

Situation Predict what the galvanometer needle does. What the needle actually does.
The magnet is moved toward the coil. No basis for prediction. Needle deflects to the left.
The magnet is moved away from the coil. Opposite to the above. Needle deflects to the right.
The magnet is moved toward the coil again, but more slowly.
The magnet is held at rest near the coil.
The magnet is held at rest and the coil is moved toward the magnet.
10
Observations with a magnet, coil, and galvanometer

• Lets make a few observations, using a magnet
  near a coil connected to a galvanometer (a
  sensitive current meter). The magnets north pole
  points at the coil.

Situation Predict what the galvanometer needle does. What the needle actually does.
The magnet is moved toward the coil. No basis for prediction. Needle deflects to the left.
The magnet is moved away from the coil. Opposite to the above. Needle deflects to the right.
The magnet is moved toward the coil again, but more slowly. Same as the first case, but needle deflects less.
The magnet is held at rest near the coil.
The magnet is held at rest and the coil is moved toward the magnet.
11
Observations with a magnet, coil, and galvanometer

• Lets make a few observations, using a magnet
  near a coil connected to a galvanometer (a
  sensitive current meter). The magnets north pole
  points at the coil.

Situation Predict what the galvanometer needle does. What the needle actually does.
The magnet is moved toward the coil. No basis for prediction. Needle deflects to the left.
The magnet is moved away from the coil. Opposite to the above. Needle deflects to the right.
The magnet is moved toward the coil again, but more slowly. Same as the first case, but needle deflects less. Needle deflects a little bit to the left.
The magnet is held at rest near the coil.
The magnet is held at rest and the coil is moved toward the magnet.
12
Observations with a magnet, coil, and galvanometer

• Lets make a few observations, using a magnet
  near a coil connected to a galvanometer (a
  sensitive current meter). The magnets north pole
  points at the coil.

Situation Predict what the galvanometer needle does. What the needle actually does.
The magnet is moved toward the coil. No basis for prediction. Needle deflects to the left.
The magnet is moved away from the coil. Opposite to the above. Needle deflects to the right.
The magnet is moved toward the coil again, but more slowly. Same as the first case, but needle deflects less. Needle deflects a little bit to the left.
The magnet is held at rest near the coil. ??
The magnet is held at rest and the coil is moved toward the magnet.
13
Observations with a magnet, coil, and galvanometer

• Lets make a few observations, using a magnet
  near a coil connected to a galvanometer (a
  sensitive current meter). The magnets north pole
  points at the coil.

Situation Predict what the galvanometer needle does. What the needle actually does.
The magnet is moved toward the coil. No basis for prediction. Needle deflects to the left.
The magnet is moved away from the coil. Opposite to the above. Needle deflects to the right.
The magnet is moved toward the coil again, but more slowly. Same as the first case, but needle deflects less. Needle deflects a little bit to the left.
The magnet is held at rest near the coil. ?? Nothing!
The magnet is held at rest and the coil is moved toward the magnet.
14
Observations with a magnet, coil, and galvanometer

• Lets make a few observations, using a magnet
  near a coil connected to a galvanometer (a
  sensitive current meter). The magnets north pole
  points at the coil.

Situation Predict what the galvanometer needle does. What the needle actually does.
The magnet is moved toward the coil. No basis for prediction. Needle deflects to the left.
The magnet is moved away from the coil. Opposite to the above. Needle deflects to the right.
The magnet is moved toward the coil again, but more slowly. Same as the first case, but needle deflects less. Needle deflects a little bit to the left.
The magnet is held at rest near the coil. ?? Nothing!
The magnet is held at rest and the coil is moved toward the magnet. Same as the first case.
15
Observations with a magnet, coil, and galvanometer

• Lets make a few observations, using a magnet
  near a coil connected to a galvanometer (a
  sensitive current meter). The magnets north pole
  points at the coil.

Situation Predict what the galvanometer needle does. What the needle actually does.
The magnet is moved toward the coil. No basis for prediction. Needle deflects to the left.
The magnet is moved away from the coil. Opposite to the above. Needle deflects to the right.
The magnet is moved toward the coil again, but more slowly. Same as the first case, but needle deflects less. Needle deflects a little bit to the left.
The magnet is held at rest near the coil. ?? Nothing!
The magnet is held at rest and the coil is moved toward the magnet. Same as the first case. Needle deflects to the left.
16
Observations with a magnet, coil, and galvanometer

• Lets make a few more observations.

Situation Predict what the galvanometer needle does. What the needle actually does.
The magnet is reversed, so the south pole points at the coil. The magnet is moved toward the coil.
The magnet is moved away from the coil.
The magnet is taken to the other end of the coil, and the north pole is closer to the coil. The magnet is moved toward the coil.
The magnet is moved away from the coil.
The magnet is rotated back and forth near the end of the coil
17
Observations with a magnet, coil, and galvanometer

• Lets make a few more observations.

Situation Predict what the galvanometer needle does. What the needle actually does.
The magnet is reversed, so the south pole points at the coil. The magnet is moved toward the coil. Opposite to when the north pole was pointed at the coil.
The magnet is moved away from the coil.
The magnet is taken to the other end of the coil, and the north pole is closer to the coil. The magnet is moved toward the coil.
The magnet is moved away from the coil.
The magnet is rotated back and forth near the end of the coil
18
Observations with a magnet, coil, and galvanometer

• Lets make a few more observations.

Situation Predict what the galvanometer needle does. What the needle actually does.
The magnet is reversed, so the south pole points at the coil. The magnet is moved toward the coil. Opposite to when the north pole was pointed at the coil. The needle deflects to the right.
The magnet is moved away from the coil.
The magnet is taken to the other end of the coil, and the north pole is closer to the coil. The magnet is moved toward the coil.
The magnet is moved away from the coil.
The magnet is rotated back and forth near the end of the coil
19
Observations with a magnet, coil, and galvanometer

• Lets make a few more observations.

Situation Predict what the galvanometer needle does. What the needle actually does.
The magnet is reversed, so the south pole points at the coil. The magnet is moved toward the coil. Opposite to when the north pole was pointed at the coil. The needle deflects to the right.
The magnet is moved away from the coil. Opposite to the above.
The magnet is taken to the other end of the coil, and the north pole is closer to the coil. The magnet is moved toward the coil.
The magnet is moved away from the coil.
The magnet is rotated back and forth near the end of the coil
20
Observations with a magnet, coil, and galvanometer

• Lets make a few more observations.

Situation Predict what the galvanometer needle does. What the needle actually does.
The magnet is reversed, so the south pole points at the coil. The magnet is moved toward the coil. Opposite to when the north pole was pointed at the coil. The needle deflects to the right.
The magnet is moved away from the coil. Opposite to the above. The needle goes left.
The magnet is taken to the other end of the coil, and the north pole is closer to the coil. The magnet is moved toward the coil.
The magnet is moved away from the coil.
The magnet is rotated back and forth near the end of the coil
21
Observations with a magnet, coil, and galvanometer

• Lets make a few more observations.

Situation Predict what the galvanometer needle does. What the needle actually does.
The magnet is reversed, so the south pole points at the coil. The magnet is moved toward the coil. Opposite to when the north pole was pointed at the coil. The needle deflects to the right.
The magnet is moved away from the coil. Opposite to the above. The needle goes left.
The magnet is taken to the other end of the coil, and the north pole is closer to the coil. The magnet is moved toward the coil. Same as the south pole at the other end?
The magnet is moved away from the coil.
The magnet is rotated back and forth near the end of the coil
22
Observations with a magnet, coil, and galvanometer

• Lets make a few more observations.

Situation Predict what the galvanometer needle does. What the needle actually does.
The magnet is reversed, so the south pole points at the coil. The magnet is moved toward the coil. Opposite to when the north pole was pointed at the coil. The needle deflects to the right.
The magnet is moved away from the coil. Opposite to the above. The needle goes left.
The magnet is taken to the other end of the coil, and the north pole is closer to the coil. The magnet is moved toward the coil. Same as the south pole at the other end? The needle deflects to the right.
The magnet is moved away from the coil.
The magnet is rotated back and forth near the end of the coil
23
Observations with a magnet, coil, and galvanometer

• Lets make a few more observations.

Situation Predict what the galvanometer needle does. What the needle actually does.
The magnet is reversed, so the south pole points at the coil. The magnet is moved toward the coil. Opposite to when the north pole was pointed at the coil. The needle deflects to the right.
The magnet is moved away from the coil. Opposite to the above. The needle goes left.
The magnet is taken to the other end of the coil, and the north pole is closer to the coil. The magnet is moved toward the coil. Same as the south pole at the other end? The needle deflects to the right.
The magnet is moved away from the coil. Opposite to the previous.
The magnet is rotated back and forth near the end of the coil
24
Observations with a magnet, coil, and galvanometer

• Lets make a few more observations.

Situation Predict what the galvanometer needle does. What the needle actually does.
The magnet is reversed, so the south pole points at the coil. The magnet is moved toward the coil. Opposite to when the north pole was pointed at the coil. The needle deflects to the right.
The magnet is moved away from the coil. Opposite to the above. The needle goes left.
The magnet is taken to the other end of the coil, and the north pole is closer to the coil. The magnet is moved toward the coil. Same as the south pole at the other end? The needle deflects to the right.
The magnet is moved away from the coil. Opposite to the previous. The needle goes left.
The magnet is rotated back and forth near the end of the coil
25
Observations with a magnet, coil, and galvanometer

• Lets make a few more observations.

Situation Predict what the galvanometer needle does. What the needle actually does.
The magnet is reversed, so the south pole points at the coil. The magnet is moved toward the coil. Opposite to when the north pole was pointed at the coil. The needle deflects to the right.
The magnet is moved away from the coil. Opposite to the above. The needle goes left.
The magnet is taken to the other end of the coil, and the north pole is closer to the coil. The magnet is moved toward the coil. Same as the south pole at the other end? The needle deflects to the right.
The magnet is moved away from the coil. Opposite to the previous. The needle goes left.
The magnet is rotated back and forth near the end of the coil The needle goes back and forth, too.
26
Observations with a magnet, coil, and galvanometer

• Lets make a few more observations.

Situation Predict what the galvanometer needle does. What the needle actually does.
The magnet is reversed, so the south pole points at the coil. The magnet is moved toward the coil. Opposite to when the north pole was pointed at the coil. The needle deflects to the right.
The magnet is moved away from the coil. Opposite to the above. The needle goes left.
The magnet is taken to the other end of the coil, and the north pole is closer to the coil. The magnet is moved toward the coil. Same as the south pole at the other end? The needle deflects to the right.
The magnet is moved away from the coil. Opposite to the previous. The needle goes left.
The magnet is rotated back and forth near the end of the coil The needle goes back and forth, too. What we said.
27
Faradays Law

• Faraday's Law ties all of our observations into
  one neat package. It says that the voltage
  induced in a coil of N turns is given by the rate
  of change of the magnetic flux in the coil
• Faraday's Law
• This has an incredible number of practical
  applications, particularly in the generation and
  distribution of electricity.
• We call the voltage induced by a changing
  magnetic flux an induced emf. This is because
  changing magnetic flux acts like a battery in a
  coil or loop, which is why there is a current
  when there's a complete circuit.

28
Graphs of flux and induced emf

• In this situation, a bar magnet is moved at
  constant speed v toward a coil until the left end
  of the magnet is at the center of the coil. The
  magnet is held stationary for 3 seconds, and then
  moved to the right away from the coil with a
  speed v.
• What does the graph of magnetic flux as a
  function of time look like? Assume positive flux
  corresponds to field lines passing through the
  coil to the left.
• What does the graph of induced emf as a function
  of time look like?

29
Lenzs Law

• Exposing a coil or loop to a changing magnetic
  flux will generate a current if the circuit is
  complete. The direction of the current is given
  by Lenz's Law
• Lenz's Law A changing magnetic flux induces an
  emf that produces a current which sets up a
  magnetic field that tends to oppose whatever
  produced the change.
• Coils and loops don't like to change, and they
  will try to counteract any changes in magnetic
  flux imposed on them. They are not successful -
  the change can be made, but the coil or loop
  tries to oppose the change while the change is
  taking place. This tendency to oppose is why
  there is a minus sign in Faraday's Law.

30
A pictorial approach to Lenzs Law

• An easy way to approach Lenzs Law situations, to
  figure out the direction of an induced current,
  it to draw a set of three pictures.
• First, some review. In which direction is the
  magnetic field inside a loop if the loop has a
  counter-clockwise current? What if the current is
  clockwise?

31
A pictorial approach to Lenzs Law

• An easy way to approach Lenzs Law situations, to
  figure out the direction of an induced current,
  it to draw a set of three pictures.
• First, some review. In which direction is the
  magnetic field inside a loop if the loop has a
  counter-clockwise current? What if the current is
  clockwise?

32
A pictorial approach to Lenzs Law

• Example A wire loop in the plane of the page is
  in a uniform magnetic field directed into the
  page. Over some time interval, the field is
  doubled. What direction is the induced current in
  the loop while the field is changing?
• Step 1 Draw a Before picture, showing the
  field passing through the loop before the change
  takes place.
• Step 2 Draw an After picture, showing the
  field passing through the loop after the change.
• Step 3 Draw a To Oppose picture, showing the
  direction of the field the loop creates to oppose
  the change.
• Step 4 Use the right-hand rule to determine
  which way the induced current goes in the loop to
  create that field.

33
A pictorial approach to Lenzs Law

• Example A wire loop in the plane of the page is
  in a uniform magnetic field directed into the
  page. Over some time interval, the field is
  doubled. What direction is the induced current in
  the loop while the field is changing?
• Step 1 Draw a Before picture, showing the
  field passing through the loop before the change
  takes place.

34
A pictorial approach to Lenzs Law

• Example A wire loop in the plane of the page is
  in a uniform magnetic field directed into the
  page. Over some time interval, the field is
  doubled. What direction is the induced current in
  the loop while the field is changing?
• Step 2 Draw an After picture, showing the
  field passing through the loop after the change.

35
A pictorial approach to Lenzs Law

• Example A wire loop in the plane of the page is
  in a uniform magnetic field directed into the
  page. Over some time interval, the field is
  doubled. What direction is the induced current in
  the loop while the field is changing?
• Step 3 Draw a To Oppose picture, showing the
  direction of the field the loop creates to oppose
  the change.
• Step 4 Use the right-hand rule to determine
  which way the induced current goes in the loop to
  create that field.
• One field line is enough for the To Oppose
  picture - that's enough to determine the
  direction of the induced current.

36
Lenzs Law example 1
A wire loop is located near a long straight
current-carrying wire. The current in the wire is
directed to the right. With the current held
constant in the long straight wire, the loop is
moved up, away from the wire. In what direction
is the induced current in the loop? 1. The
induced current is clockwise. 2. The induced
current is counter-clockwise. 3. There is no
induced current.
37
Lenzs Law example 1

• The flux through the loop decreases, so the loop
  tries to add field lines that are directed out of
  the page to oppose the change. The induced
  current must go counter-clockwise to produced the
  required field.

38
Lenzs Law example 2
With the current held constant in the long
straight wire, the loop is moved parallel to the
wire. In what direction is the induced current in
the loop? 1. The induced current is clockwise.
2. The induced current is counter-clockwise. 3.
There is no induced current.
39
Lenzs Law example 2

• The flux through the loop is constant, so there
  is no change to oppose, and no induced current.

40
Lenzs Law example 3
The loop is now placed directly on the wire with
the wire bisecting the loop. If the current in
the wire is increasing, in what direction is the
induced current in the loop? 1. The induced
current is clockwise. 2. The induced current is
counter-clockwise. 3. There is no induced
current.
41
Lenzs Law example 3

• The net flux through the loop is always zero, so
  there is no change to oppose, and no induced
  current.

42
Lenzs Law example 4
A loop of wire, in the plane of the page, has an
area of 0.5 m2 and a resistance of R 0.1 O.
There is a uniform magnetic field of B 1.0 T
passing through the loop into the page. In what
direction is the induced current in the loop? 1.
The induced current is clockwise. 2. The induced
current is counter-clockwise. 3. There is no
induced current.
43
Lenzs Law example 4

• Nothing is changing, so there is no induced
  current.

44
Lenzs Law example 4, continued
A loop of wire, in the plane of the page, has an
area of 0.5 m2 and a resistance of R 0.1 O.
There is a uniform magnetic field of B 1.0 T
passing through the loop into the page. Now the
magnetic field is reduced steadily from 1.0 T to
0 over a 10 second period. In what direction is
the induced current in the loop? 1. The induced
current is clockwise. 2. The induced current is
counter-clockwise. 3. There is no induced
current.
45
Lenzs Law example 4, continued

• The pictorial method tells us that the field from
  the loop must be into the page, requiring a
  clockwise current.

46
Lenzs Law example 4, continued

• A loop of wire, in the plane of the page, has an
  area of 0.5 m2 and a resistance of R 0.1 O.
  There is a uniform magnetic field of B 1.0 T
  passing through the loop into the page. Now the
  magnetic field is reduced steadily from 1.0 T to
  0 over a 10 second period. In what direction is
  the induced current in the loop?
• What is the magnitude of the induced current in
  the loop?

47
Lenzs Law example 4, continued

• A 0.5 m2 R 0.1 O Bi 1.0 T
• Now the magnetic field is reduced steadily from
  1.0 T to 0 over a 10 second period.
• First, apply Faradays law to find the induced
  emf (voltage)

48
Lenzs Law example 4, continued

• A 0.5 m2 R 0.1 O Bi 1.0 T
• Second, apply Ohms law to find the current

49
Lenzs Law example 4, continued

• If we'd kept the magnetic field constant, what
  other ways could we have induced the same current
  (magnitude and direction) in the loop?

50
Lenzs Law example 4, continued

• If we'd kept the magnetic field constant, what
  other ways could we have induced the same current
  (magnitude and direction) in the loop?
• By changing the field we reduced the flux to zero
  over a 10 second period. Two other ways to do
  that are
• reduce the area to zero over a 10 second interval
  
• rotate the loop by 90 over a 10 second interval

51
Lenzs Law example 4, continued

• What if, instead of reducing the field to zero in
  10 seconds, we reduced it to zero in 2 seconds?
  Would anything change? Would anything stay the
  same?

52
Lenzs Law example 4, continued

• What if, instead of reducing the field to zero in
  10 seconds, we reduced it to zero in 2 seconds?
  Would anything change? Would anything stay the
  same?
• The current would still be clockwise, but it
  would be 5 times as large. So, we'd get five
  times the current for 1/5 of the time. The
  product of current and time would be the same,
  but that represents the total charge. The same
  total charge flows every time.

53
Graphs of flux and induced current

• A square conducting loop moves at a constant
  velocity of 1 m/s to the right. At t 0, its
  right side is at x -6 m. A region of uniform
  magnetic field directed into the page is located
  between x  -4 m and x 0. A second region of
  uniform magnetic field directed out of the page
  is located between x 0 and x 4 m. The field
  in the two regions has the same magnitude and the
  field is zero everywhere else. Assume the
  velocity of the loop is constant throughout its
  motion. Simulation

54
Graphs of flux and induced current

• A square conducting loop moves at a constant
  velocity of 1 m/s to the right. At t 0, its
  right side is at x -6 m. A region of uniform
  magnetic field directed into the page is located
  between x  -4 m and x 0. A second region of
  uniform magnetic field directed out of the page
  is located between x 0 and x 4 m. Plot graphs
  of the magnetic flux through the loop, and the
  induced current in the loop, as a function of
  time. Define into the page as positive for flux,
  and clockwise to be positive for current.

55
The flux graph

• Remember that flux is a measure of the number of
  field lines passing through the loop, with
  positive for, in this case, field lines into the
  page.

56
The graph of induced current

• What is the connection between the graphs?

57
The graph of induced current

• What is the connection between the graphs? The
  current graph is proportional to the negative
  slope of the flux graph.

58
Whiteboard