Download PHY 142L Spr 2016 Lab 4

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Flux and Faraday’s Law
E
lectromagnetic induction – the creation of an electric current by a changing magnetic field – was first
observed by Michael Faraday and Joseph Henry in 1831. (Faraday published first.) Since that time,
that phenomenon and other closely related ones have become central to modern life. Induction plays a
crucial role in electric power generation, information storage, medical imaging, and many other activities.
In this lab we will first use software to simulate and visualize the mechanism of induction. Afterward, we will
use physical coils, bar magnets and moving carts to generate EMFs in wires and compare them to known
features of the changing magnetic flux in our setup.
Computer Investigation
In this investigation we will use a Java application to visualize the process of electromagnetic induction.
The goal is for you to develop a visual image of exactly how changes in a magnetic field can result in
induced currents, which will help you interpret the mathematical expressions we use to do more
quantitative calculations.
Recall from your coursework that a loop of wire in a magnetic field will intercept some amount of
magnetic flux:
ZZ
B
~ · dS
~
B
=
The double integral sign indicates that we are summing the B field over the 2D
area enclosed by the wire loop. For a planar loop in a constant magnetic field,
this simplifies to:
B
~ ·A
~ = BA cos ✓,
=B
where A is the area of the wire loop, and the direction of the area vector is
perpendicular to the plane of the loop.* When induced current flows in the
wire loop, we will use the right hand rule and refer to the direction of
to
know which direction of flow is positive or negative.
Faraday's Law states when the flux through the loop changes, there will be an EMF around the loop:
EMF =
d B
dt
If the coil of wire has N turns (rather than just one), then the area enclosed (and therefore the enclosed
flux) is effectively multiplied by a factor of N. Think of it as the sum of N separate loops.
* It is a remarkable fact that the value of the integral will not depend on exactly which surface you use, as long as the
wire forms the boundary of the surface! Usually it is easiest to consider the simple case in which the surface is the planar
disk bounded by the wire, but we could imagine a surface that bubbles out of the plane and the equation above would
still be right.
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• Working in pairs at your station, open a web browser and go to the following URL:
http://phet.colorado.edu/en/simulation/faradays-law
Run the simulation now. Once it is running, make certain to "show field lines."
You should see a simulated wire coil connected to a voltage meter and a light bulb, as well as a bar
magnet that you can move. As you move the bar magnet, pay close attention to the field lines intersecting
the coil's area. Remember that the magnitude of induced voltage is the magnitude of the rate of change
of the flux. Make sure you see
• As shown in the illustration, move the North
pole of the magnet across the coil's area by dragging
vertically it at a constant speed. Describe what you
observe by filling in the table below:
This table assumes you are moving the magnet
from the bottom to the top of the screen.
Event
Magnet pole crosses
lower edge of coil
Observation
Magnet pole moves
across coil's area
Magnet pole crosses
upper edge of coil
Magnet pole is moving,
but outside of coil's area
•
Based on your observations in this simulation, use the axes below to sketch the magnetic flux ΦB
through the coil as a function of time⎯assuming the magnet moves vertically at constant velocity:
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•
On the axes below, use your sketch (above) of ΦB to create a sketch of -(dΦB/dt).
[Tip: Recall from a previous physics course how you sketched velocity (dx/dt) based on a plot
of position. The same skills will apply!]
•
How does this sketch relate to the behavior of the meter in the simulation?
Close this simulation and open up the following link with your browser:
http://phet.colorado.edu/en/simulation/faraday
Run this simulation now. A new window should appear. This software contains several tabs simulating
different scenarios.
Click on the Bar Magnet tab. You see a visualization of the field of the bar magnet. Adjust the field
strength to get a feel for how the simulation shows this parameter. Click the box "See Inside Magnet".
Now click the Generator tab. This simulation shows a magnet spun on a water wheel. By adjusting the
control on the water tap (located towards the upper left of the screen) you can change the rate at which
the magnet rotates. Click the "show field" checkbox and start the magnet rotating at a moderate speed.
•
Notice that the simulation shows charges within the wire coil. How do the charges behave
as the magnet rotates?
•
Use Faraday's Law to explain why the charges are behaving in this way (in other words, why
do they not move in one direction at constant speed, or simply remain at rest?) You are
encouraged to discuss the effect with other groups and compare notes. Later on, you will be
able to investigate this phenomenon with the equipment at your station.
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Experimental Investigation 1
At your station, an aluminum track runs parallel to the face of a wire coil. On the track is a cart. A clamp
on this cart can hold one or more bar magnets. The cart will carry the magnets so that their poles move
across the wire coil.
Magnet in clamp
Coil
Predictions
Assume that you give the cart an initial push, and one pole of the magnet moves across the face of the coil
at constant velocity as the arrow illustrates above. Predictions must be done in ink. Remember, the goal
of predictions is to examine your own understanding of physics; there are no right or wrong answers, but
you are graded on the basis of giving due thought.
•
This scenario is almost identical to the first simulation you looked at. Your sketched graphs from
that simulation are predictions for the flux ΦB(t) and the induced voltage in this experiment.
•
Predict how the peak flux will change if ⎯instead of using one bar magnet⎯the cart passes
across the coil carrying two side-by-side bar magnets with their N and S poles pointing the same
direction (this may require some velcro straps because they will repel each other).
•
What would happen to your plot of flux if you reverse the poles of the magnet (e.g. if the N pole
was originally pointing towards the coil, now orient the S pole toward the coil)?
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•
On the axes below, predict the shape of the induced voltage as a function of time if the cart passes
through the coils carrying two side-by-side bar magnets with their poles pointing in opposite
directions.
•
One last prediction: Imagine, as before, that the cart is pushed past the coils carrying one magnet.
How will the EMF induced by a slow-moving cart compare to that of a fast-moving cart? Will
the peak voltage be less, greater, or the same?
Test your predictions
Open the Lenz.cmbl data acquisition file to collect voltage data from the coils. Remember to zero your
voltage reading! Your sensor will still probably drift, so you can use the Offset control on-screen to shift
your plot upward or downward, to center it on the axis. You should see a plot of flux in addition to
voltage. Since this plot is found by integrating the voltage, you will know that your Offset is correct
when the flux plot does not have an overall increasing or decreasing trend as a function of time.
•
Test each of your predictions and obtain good plots of each situation by zooming in where
appropriate. Attach each plot to this lab report with a brief typed summary of how it agrees (or
differs) from what you expected. Keep your data from the last prediction stored in Logger Pro.
•
Explain the reason that the voltage curve for one magnet looks like it does. Use arguments based
on induction and flux. You may keep any of the simulations open to aid your thinking. Use
relevant equations.
•
When you used two magnets pointing in opposite directions, what happened? How does
Faraday's Law explain this?
•
Return to your data for the slow and fast moving carts. Find the area under the positive part (or
negative part – as long as you are consistent) of the voltage curve for each situation. What is the
percent change in the area between fast and slow runs? Is this change very significant, possibly
significant, or insignificant? Use what you have learned to formulate an explanation for this
result.
•
PHYSICALLY, what is the area under this curve? (Example: on a velocity vs. time graph, the
area under the curve is Velocity x Time = Distance Traveled).
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Experimental Investigation 2
At your table, you should have a small metal stand that is able to spin. (If you do not have a
stand, your TA will give you one.) Your bar magnet ought to rest comfortably in this stand.
This experiment replicates the second simulation (this time, the magnet will be
spun by hand rather than by a water-wheel).
Set the stand (with bar magnet) near one end of your coil as shown in the
illustration below. Zero your sensor, and begin collecting data. Then, spin the
magnet. If everything is centered, your sensor will display a smooth, regular
waveform. Print out your data for your report.
A bar magnet in the
stand. This will allow the
magnet to spin freely.
•
What kind of waveform is produced when the bar magnet
spins? [Do you expect it to be a perfect sine wave? Sketch a
picture of the field lines created by the magnet when it is at
angles of 0, 45, and 90 degrees to the axis of the coils, as seen
from above.]
•
When the voltage is at its peak value, how much magnetic
flux passes through the coil's area? What kind of waveform
is represented by the plot of the flux?
•
Why does the induced voltage behave in this regular way - physically, what is going on?
•
Does the behavior of this experiment seem consistent with the simulation you saw earlier?
CHALLENGE: The second-simplest motor imaginable
Recall from the Magnetic Force lab that you could make a motor by allowing a stationary magnetic to
create forces on an intermittent current in a spinning loop of wire. It stands to reason (by Newton’s Third
Law) that we should be able to use an intermittent (or alternating) current to create forces on a magnet
and get it to spin. So let’s see if we can make a magnet spin by manipulating the current in the coil.
(1) Place the magnet about 20cm away from the coil, roughly on the coil axis. Now connect the coil to a
DC power supply. Use one red wire and make the black wire run from the power supply to a switch, and
then to the coil, so that you can turn the current on or off using the switch. Set the power supply voltage
to 0.5 V. Now close the switch and watch the magnet. The challenge is to make magnet spin as fast as
possible without touching it (or blowing on it). Can you make it spin at all? Let everyone try.
Congratulations! You just made a very inefficient, slow motor.
(2) Now let’s use an AC power supply that can reverse the current at rates much faster than you can go
by hand. Hook up the coil to the small AC power supply at your station (ask your TA for assistance) and
see how fast you can get the magnet to spin. You should be able to get it to turn at more than 10 cycles
per second. Show your TA your best result.
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