Download Lab 12: Faraday`s Effect

Physics 272 Lab
Lab 12: Faraday’s Effect
Lab 12: Faraday’s Effect
OBJECTIVES
In this part of the lab you will:
 Use Faraday’s law to predict the emf produced in a coil from a time-varying magnetic field
 Measure the emf produced in a coil for a time-varying magnetic field
Faraday’s law states that a changing magnetic flux will produce an electric field according to:
∮ ⃗
(∫ ⃗
̂
)
If you place a coil with appropriate orientation in the region of this changing magnetic field, the
electric field will cause a voltage difference between the ends of the coil. In this lab you create a
changing magnetic field by moving a bar magnet away from a coil, and measure the resulting
potential difference (emf). Before you make the measurement, you will attempt to calculate
what the emf will be.
1) Warm—Up Problem
Problem #1 The north pole of a bar magnet points toward a thin circular coil of wire
containing 40 turns. The magnet is moved away from the coil, so that the flux through
one turn inside the coil decreases by
0.3 Tm2 in a time
0.2s. What is the
average emf induced in the coil during this time interval? Viewed from the right side
(opposite the bar magnet), does the induced current run clockwise or counterclockwise?
Explain briefly.
CHECKPOINT 1: Ask an instructor to check your work for credit. You may proceed
while you wait to be checked off
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Physics 272 Lab
Lab 12: Faraday’s Effect
2) Predicting the emf
a) Take out the following items for this part of the lab
1 compass
1 bar magnet
1 ruler or meter stick
1 coil of 1600 turns
1 PASport voltage sensor
b) Quickly determine and record the magnetic dipole moment of the bar magnet in
your kit. If you do not remember how to do this from Lab 8, you can do this with a
compass and a ruler:
The magnetic field on the axis of the bar magnet is given by:
Baxis =
μ 0 2μ
,
4π r 3
where μ is the called the magnetic dipole moment. It is an intrinsic and fixed quantity for the bar
magnet. Calculate μ for your bar magnet by measuring the deflection angle, , that your compass
makes when it is a distance, , from the magnet. Recall that the magnetic field, | ⃗ |, can be
obtained by relating the magnetic field of the magnet to the magnetic field of the Earth.
Recall: The horizontal component of the Earth’s magnetic field is
T
c) Determine the average flux through one turn of the coil (read on for details).
Hold the bar magnet so the end of the magnet is just outside the coil, as shown below. This will
be the initial position. Now hold your magnet approximately 30 cm away from the coil. This is
your final position. You need to calculate the approximate magnetic flux through one turn of the
coil, due to the magnet at each of these locations, and then find the total flux through all the turns
of the coil. To do this, we will first calculate the average area of one turn of the coil.
~30 cm
Magnet
Coil
Magnet
Coil
(Initial Position)
(Final Position)
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Physics 272 Lab
Lab 12: Faraday’s Effect
d) Determine the average area through one turn of the coil.
If you examine your 1600 turn coil, you will notice that the inside and outside diameters of the
coil are rather different (See figure below).
w
If you take the coil to be a square with internal width and height
, then the average area is given by,
A=
and outside width and height
W 3 -w 3
,
3  W-w 
This expression is obtained by using the average value of a function, ̅ on an interval
defined as:
̅
∫
to
( )
Therefore the average area, ̅, is given by:
̅
∫
̅
∫
̅
[
( )
| ]
Now, measure the values of and
for your coil, and calculate the average area of 1 turn. Is
your answer reasonable? Check to make sure that the area you calculated is larger than
and
less than
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Physics 272 Lab
Lab 12: Faraday’s Effect
e) Determine the average magnetic field inside the coil from the bar magnet, by
deriving a formula in the same way we derived the formula for average area.
Recall that the magnitude of the magnetic field of a bar magnet on axis is:
Since some of the turns in the coil are closer to the bar magnet than others, the magnetic field
will vary throughout the coil (see figure below). Derive the average magnetic field through one
turn of the coil. Hint: the lower limit of the integral is l, the distance from the center of the
magnet to the front of the coil. The upper limit of the integral is L, the distance from the center of
the magnet to the far end of the coil. The function you should be integrating is ( )
𝑙
Magnet
Coil
Now, measure the values of and
turn. Is your answer reasonable?
(Initial Position)
for your coil, and calculate the average magnetic field of 1
f) Determine the average magnetic flux through one turn of the coil in the initial
situation.
g) Determine the average magnetic flux through all turns of the coil in the initial
situation.
Now for the final situation when the magnet is approximately 30 cm away,
h) Determine the average magnetic field inside the coil from the bar magnet.
i) Determine the average magnetic flux through one turn of the coil in the final
situation.
j) Determine the average magnetic flux through all turns of the coil.
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Physics 272 Lab
Lab 12: Faraday’s Effect
Now, you want to move the magnet rapidly away from the coil so that the change in flux over
time is large. A typical time for rapidly moving your hand 30 cm is
0.05 s. There is a
motion sensor attached to the TA’s computer where you can check how fast you can move your
hand if you wish.
k) Use the typical ∆t = 0.05 s (or the time you measured for ∆t) along with the change
in flux from initial to final position, to predict the emf you should observe when you
quickly move the magnet from near the coil to 30 cm away.
What is your predicted value for the induced emf ?
CHECKPOINT 2: Ask an instructor to check your work for credit. You may proceed
while you wait to be checked off
3) Measuring the emf
a) Log on to the lab computer and open faraday.ds
b) Connect the PASport voltage sensor cables to the coil.
c) Click “START” to start recording, and move the magnet back and forth a few times
to see what happens.
d) Move the magnet slowly.
e) Describe qualitatively what you observe.
f) Move the magnet rapidly.
g) Describe qualitatively what is different in your observations.
h) Now measure the peak emf in the coil when you move the magnet away rapidly
several times (you do not need to stop your hand when it is 30 cm away). Start at the
initial location you used in your prediction calculation.
i) Draw a sketch of a typical peak with scale and units in your work space
j) Compare your experimental value to your predicted value.
k) Give the approximations you made in estimating the emf.
Are your measured and predicted values in good agreement? If not, try to explain why.
CHECKPOINT 3: Ask an instructor to check your work for credit. You may proceed
while you wait to be checked off
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