PHYS 2426 – Engineering Physics
II
The Magnetic
Field of a Solenoid
Leader:
___________________ Recorder:
__________________________
Skeptic:
___________________ Encourager:
________________________
LabPro
Magnetic Field Probe
3 Two ring stands with right
angle clamps
1 x jaw clamp
Meter stick
Masking Tape
Slinky
Cow magnet
Compass
10 A, 28 V DC Power Supply
In this lab we will investigate the
magnetic field of the solenoid.
Procedure
1. Familiarize Yourself with the Magnetic Field
Sensor
Make sure that the switch on the magnetic
field sensor is set on LOW. Use a
compass to identify the north pole of a cow magnet. Remember the north pole of the compass needle
points to geographic north. Thus the
north pole of a bar magnet will be repelled by the north pole of a bar magnet.
Label the North pole of the bar magnet for later reference.
Plug the magnetic field sensor into CH 1
of the LabPro and connect the LabPro to the computer. Launch LoggerPro and open
the experiment file “Mag lo mT” by following the path Probes &
Sensors=>Magnetic Field=>Mag lo mT
Clamp the magnetic field sensor to a ring
stand with a test tube clamp or jaw clamp.
Hold the north pole of the bar magnet up to the end of the magnetic
field sensor with the white dot on it.
Press collect and the computer will display a graph of the magnetic
field strength vs. time. Observe the
orientation of the sensor compared to the magnet when it gives a maximum
positive value.
Q1) How should the magnetic field sensor be
oriented so that it reads a maximum positive value when the north pole of a
magnet is directed towards it?
2. Set Up
Slip the provided slinky over a meter
stick and suspend the meter stick on clamps between two ring stands so that the
slinky is off the table. Tape the ends
of the slinky to the meter stick so that the slinky is stretched 50 cm. Attach
either side of the slinky to the high current DC power supply with the provided
alligator clips.
Q2) Based on the + and - terminals on the power
supply, if you curl your fingers of your right hand in the direction of the
current what direction does your thumb point (e.g. left or right) along the
axis of the solenoid.?
3.
Data Acquisition
Turn on the power supply and adjust the DC
current to 1 A. Position the magnetic
field sensor inside the middle of the solenoid and rotate it so that it reads a
positive maximum value. Gently clamp the
sensor in the position where it reads the maximum positive value.
Q3. If
you curl your fingers of your right hand in the direction that the current flows
around the solenoid, what direction does the north pole of the magnetic field
point (left or right)?
This result is a right hand rule
for determining the direction of the magnetic field of a solenoid. When you curl your fingers of your right hand
in the direction that the current flows around the solenoid, your thumb points
in the direction of the magnetic field.
4. Vary the Current
Since the fields we will be measuring will
be comparable to the local magnetic field of the Earth, we will subtract out
the background. With no current flowing through the solenoid (turn off the
power supply), zero the magnetic field sensor.
The program will average the background magnetic field and subsequently
subtract it from the data.
Run
an experiment where you vary the current from 1 – 5 A in 1 A steps. Do not
exceed 5 A. Record the current and the
average B-field strength. To obtain the average field strength, collect data
for a few seconds and then stop. Alternatively,
you can adjust the current while the data collection is running. Click and drag over a smooth section of data,
and then use the STAT button on the tool bar to obtain the mean value of the
field. Construct a graph of Field
Strength vs. Current and attach your graph to this worksheet.
Q4) How does the Magnetic field strength depend
on the current?
Now that we've seen that the magnetic
field strength of the solenoid depends linearly on the current, we would like
to see what other quantities it depends on.
On issue we can address is does the magnetic field strength remain the
same the entire length of the solenoid.
Conduct an experiment where you measure the value of the magnetic field
strength in the center of the coil at 5 cm intervals along the length of the
solenoid. Construct a graph of the
magnetic field strength versus distance along the solenoid.
Q5) Describe in words how the magnetic field
strength varies along the length of the solenoid.
Once we've determined that the magnetic
field is fairly constant along the axis inside the solenoid except possibly at
the ends, we might ask what other effects of geometry affect the magnetic field
strength of the solenoid.
One factor that may affect the magnetic
field strength is the length of the solenoid.
Conduct an experiment where you vary the length of the solenoid. Keep one end of the slinky fixed and stretch
the other end in 5 cm increments beginning at a length of 25 cm. Keep the current constant at 2 A throughout
the experiment. Construct a graph of the
magnetic field strength versus the length.
Q6) Based on your prior experience, what type of
relationship seems to be exhibited by the graph of the magnetic field strength
versus length? How can you plot the data
to more clearly demonstrate this relationship?
Another factor that might affect the
magnetic field strength is the number of turns in the slinky. Count the number of turns in your
slinky. Stretch the slinky to 30 cm.,
and measure the magnetic field at a current of 2 A. Next, reattach the wire 5 coils up along the
slinky and then reposition the slinky so that the distance between the points
at which the wires are attached is 30 cm.
Record the number of coils and measure the magnetic field strength. Repeat this procedure three more times.
Construct a graph of Magnetic Field
Strength versus the Number of coils at constant length and current.
Q7) What type of relationship does your graph
show between the magnetic field strength and the number of turns?
If we examine the results of our
experiments we find that the magnetic field of a solenoid can be given by the
following relationship B = m0 (N/L) I,
where N is the number of turns in the coil, L is the length of the coil, and I
is the current flowing in the coil. m0 is a
constant called the permeability of free space.
It is a defined quantity and has a value of exactly m0 = 4p x 10-7 Tm/A. The magnetic field strength depends on the
quantity N/L. This quantity represents
the number of turns per unit length and is typically denoted n = N/L. In terms of the turns per unit length we can
write the magnetic field of the solenoid as B = m0 n
I. A consequence of this is that as long
as the number of turn per unit length remains the same, the magnetic field strength
will remain the same.
Reposition the slinky so that it stretches
to .5 m again. Measure the magnetic
field strength for a current of 2 A.
Without disturbing the slinky, move one of the wires so that it attaches
at the midpoint of the slinky.
Q8) Predict what will be the effect on the
magnetic field strength with a current of 2 A and one of the wires at the
midpoint compared to the when the solenoid has the wires attached at .5 m
apart. Explain.
Measure
the magnetic field strength at a current of 2 A at the midpoint between the two
wires connected to the power supply.
Q9) Were you correct? If not rethink your explanation.
A Measurement of m0
From data we've already obtained, we can
determine a value of m0. The relationship between field strength and
current is B = m0 n
I. Thus when we graph B vs. I for
constant n, the slope of our graph will be slope = m0 n.
Q10) For the graph of B vs. I, find the slope of
the best fit line which goes through your data.
From that slope and the value for n determine m0.
Q11) Calculate the percent
difference between your measured value and the defined value given above.