EX-5540 Magnetic Fields Coils-1
EX-5540 Magnetic Fields Coils-1
EX-5540 Magnetic Fields Coils-1
Included:
1 Helmholtz Coil Base EM-6715
2 Field Coil (500-Turn) EM-6723
1 Primary and Secondary Coils SE-8653A
1 Patch Cords (set of 5) SE-9750
1 Patch Cords (set of 5) SE-9751
1 60 cm Optics Bench OS-8541
1 Dynamics Track Mount CI-6692
1 20 g hooked mass (Hooked Mass Set) SE-8759
1 Small Round Base (Set of 2) ME-8974A
2 25 cm Steel Rod ME-8988
1 Optics Bench Rod Clamps (Set of 2) OS-8479
1 2-Axis Magnetic Field Sensor PS-2162
1 Rotary Motion Sensor PS-2120
Required, but not included:
1 850 Universal Interface UI-5000
1 PASCO Capstone Software
Introduction
The magnetic fields of various coils are plotted versus position as the Magnetic Field Sensor is
passed through the coils, guided by a track. The position is recorded by a string attached to the
Magnetic Field Sensor that passes over the Rotary Motion Sensor pulley to a hanging mass.
It is particularly interesting to compare the field from Helmholtz coils at the proper separation of
the coil radius to the field from coils separated at less than or more than the coil radius. The
magnetic field inside a solenoid can be examined in both the radial and axial directions.
Theory
Single Coil R
μo ∋R2
B= 3 (1)
2 2 2
2 (x +R )
Figure 1: Single Coil
Two Coils
Figure 2: Two Coils with Arbitrary Separation
R R R R
B1 B2
x
x x
R
d
For two coils, the total magnetic field is the sum of the magnetic fields from each of the coils. On
the axis we have:
B = B 1 + B2
For Helmholtz coils, the coil separation (d) equals the radius (R) of the coils. This coil separation
gives a uniform magnetic field between the coils. Plugging in x = 0 gives the magnetic field at a
point on the x-axis centered between the two coils:
B=8 μ o∋
⃗ ¿ ^x ¿ (3)
√ 125 R
Solenoid
For a long solenoid with n turns per unit length, the magnetic field is
B=μ o∋¿ . (4)
The direction of the field is straight down the axis of the solenoid.
Setup
1. Attach a single coil to the Helmholtz Base so it is aligned with the white rectangle on the
base and thus perpendicular to the base. Connect Output #1 of the 850 Universal Interface
directly across the coil as shown in Figure 4.
2. Pass the optics track through the coil and support the two ends of the track with the support
rods. One end of the optics track should be close to the edge of the table so when you hang a
mass over the Rotary Motion Sensor, it will hang freely over the edge of the table.
3. Level the track and adjust the height so the Magnetic Field Sensor probe will pass through
the center of the coil when it is pushed along the surface of the track against the side with the
yellow metric scale. An accurate way to do this is shown in Figure 5. The coil diameter is
23.4 cm. The height is adjusted (while maintaining level) so that a thin metric ruler lies just
below the holes in the side of the coil holder and 0 cm is at the edge of the coil. The track is
adjusted so that the white dot marking the axial sensor is at the 11.7 cm mark. The bottom of
the sensor probe is even with the ruler. The coil base needs to be parallel with the optics
track. Note that the coil is 2 cm wide, so the exact coil center is 1 cm from the edge of the
ruler (at 17 cm in Figure 5). When the white dot on the side of the magnetic probe is at this
point (17 cm on the yellow scale in Figure 5), the sensor is very close to the coil center.
4. Attach the Rotary Motion Sensor to the track using the bracket as in Figure 6. Cut a piece of
thread long enough to reach from the floor to the track. Tie a loop in one end of the thread
and slide the sensor probe of the Magnetic Field Sensor through it (see Figure 5). Pass the
other end of the thread over the middle step of the Rotary Motion Sensor pulley and attach
the 20-g mass. Place the Magnetic Field Sensor against the side of the track with the yellow
scale and adjust the position of the Rotary Motion Sensor so the thread is aligned with the
middle step pulley.
5. In PASCO Capstone, open the Hardware Setup and click on Signal Generator #1 and select
the Output Voltage Current Sensor.
6. Plug the Magnetic Field Sensor and the Rotary Motion Sensor into any two of the PASPORT
inputs on the 850 Universal Interface. Set the sample rate of all the sensors to 20 Hz.
7. Create a graph of Magnetic Field Strength (axial) vs. Position. Create a digits display with
the Current.
2. Find the radius of the coil by measuring the diameter from the center of the windings on one
side across to the center of the windings on the other side. Enter the value in the Coil
Properties table in the Analysis 1 section.
3. Slide the Magnetic Field Sensor along the track until the probe sensor is in the middle of the
coil. Press the tare button on the Magnetic Field Sensor. Click on Data Summary at the left of
the page. Open the properties of the Rotary Motion Sensor (RMS) by clicking on the gear
symbol to the right of the Rotary Motion Sensor label. De-select “Zero Sensor Measurement
at Start”. Click on "Zero Sensor Now". This will make zero on the x-axis be at the center of
the coil. Click OK. Click Data Summary to close the panel.
4. Slide the Magnetic Field Sensor back away from the coil until it is about 15 cm from the coil.
5. Click on Signal Generator at the left of the screen. Verify that the DC voltage is set to 15 V
and click On.
6. Click RECORD and slowly move the Magnetic Field Sensor along the track, keeping it
against the side with the yellow scale, until the end of the sensor is about 15 cm past the coil.
Then click STOP.
7. Click the DC current off in the Signal Generator. Click Data Summary. Double click Run #1
and re-label it “Single Coil”.
8. Record the Coil Current (see below) in the Coil Properties table in the Analysis 1 section.
1. For each graph, click the black triangle by the Run Select icon and select “Single Coil”.
Click the Scale-to-Fit icon.
2. For the Axial Field graph, click on the black triangle by the Curve Fit icon and select
User Defined. Click on the User Defined box that appears on the graph. The Curve Fit Editor
will appear on the Tools bar at the left of the screen.
3. Click on the Curve Fit Editor and type in the theoretical equation for the magnetic field
(Equation 1 from Theory) into the equation line where y = magnetic field strength (B) and
the other symbol are as written in Equation 1 except let m = 0. Click Apply. Enter m = 0 =
1.257e-6, the current, the coil radius, and number of turns in the coil and lock all parameters.
Click Update Fit.
4. Discuss any differences between the experimental axial curve and the theoretical fit.
5. The perpendicular field should be zero everywhere on the axis. If it isn’t, why not?
1. Attach a second coil to the Helmholtz Base at a distance from the other coil equal to the
radius of the coil. Note that you cannot just use the white rectangles on the base since it was
designed for the 200 turn coils and the 500 tern coils are have a slightly larger diameter.
Make sure the coils are parallel to each other (the white rectangles do help). See Figure 6.
The left coil is about 15 cm from the end of the track. Align coils & track as before.
2. Connect the second coil in series with the first coil. See Figures 6 & 7. Note that the
connectors on the coil all face outward and that the black jumper cable between the coils
goes from black connector to black connector. The other black cable goes from the white
connector to the black connector on the 850.
Btheory=0.5*μ₀*N*I*R²*((([Position]-d/2)²+R²)^-1.5+(([Position]+d/2)²+R²)^-1.5)
Units of T
μ₀=[Permeability constant] Units of Tm/A
I=.5 Units of A
R=0.105 Units of m
d=0.105 Units of m
2. Add Btheory to the vertical axis that has the Magnetic Field Strength (Axial) by Adding
Similar Measurement.
3. Slide the Magnetic Field Sensor back away from the coils until it is about 15 cm from the
first coil. Turn on Signal Generator #1 (15 V). Start recording and slowly move the Magnetic
Field Sensor along the center of the track, keeping the probe parallel to the track, until the
end of the sensor is about 15 cm past the second coil. Then stop recording.
4. Click open Data Summary. Double click on this run and re-label it "Helmholtz Coil".
5. Click open the Signal Generator. Click the DC voltage Off. Click Signal Generator to close
the panel.
6. Click Calculator and verify that line 1 matches Equation 2 from Theory. Change line 4 to
match the current shown in the Helmholtz Coil Current box. Change line 5 & 6 to match your
measured coil radius. d from line 6 should be the same as R from line 5.
1. Now change the separation between the coils to 1.5 times the radius of the coils. Repeat the
scan. Click open Data Summary and label this run "1.5 R".
2. Now change the separation between the coils to half the radius of the coils. Repeat the scan.
Label this run "0.5 R".
3. How does changing the coil spacing affect the magnetic field?
Solenoid Procedure:
1. Setup as shown in Figure 8 by setting the solenoid on the optics track. Note that the magnetic
sensor probe goes just past halfway thru the coil when fully inserted. The 2-axis Magnetic
Field sensor is still connected to the Rotary Motion Sensor.
3. With the DC power off, put the Magnetic Field Sensor all the way inside the solenoid. Press
the Tare button. Click open Data Summary. Click Rotary Motion Sensor properties and click
“Zero Sensor Now”. Click OK. Note the position of the solenoid on the track and try not to
move it during the rest of the experiment.
4. Click open Signal Generator. Output 1 should be set for a DC Voltage of 1 V. Click the
DC Voltage on. Click RECORD and adjust the DC Voltage until the Solenoid Current reads
about 100 mA. Click STOP. Click Delete Last Run. Click the Signal Generator closed.
5. Click RECORD. Move the sensor around inside the solenoid staying within a few cm of the
center, but moving from the axis to the edge of the coils and back. Click STOP.
6. Examine the Central Field graph. Click the Scale-to-Fit icon. Is the field inside the solenoid
the same everywhere?
7. Measure the length of the coil (between the end blocks). PASCO specs list the coil as having
2920 turns. Using this information and Equation 4 from Theory calculate the theoretical
value of the magnetic field. Click on the black triangle by the Statistics icon and select
“mean”. Click on the Statistics icon. The mean value should appear on the left of the graph.
Compare this value to the theory value.
Solenoid Field
2. Click RECORD. Move the probe slowly out of the solenoid and about 5 cm beyond.
Click STOP.
3. Note that the sensor is about 7 cm from the body of the 2 Axis Magnetic Field Sensor, so
the sensor exits the coil when the position is about 7 cm.
5. What happens to the axial field as you approach the ends of the coil?
1. Set up the single coil as before except instead of putting the track through the coil, set up the
track so it is parallel to the face of the coil. Make sure the elevation of the track is set so the
magnetic probe is at the height of the center of the coil.
2. Create a graph of the Axial Magnetic Field vs. Position and then add a second plot area for
the Perpendicular Magnetic Field vs. Position.
3. With the DC power off, slide the magnetic field sensor along the track until the end of the
Magnetic Field Sensor in the middle of the coil. Press the tare button. Also, open the
properties of the Rotary Motion Sensor in the Data Summary and click on "Zero Sensor
Now". This will make zero on the x-axis be at the center of the coil. Also uncheck "Zero on
Start".
4. Slide the Magnetic Field Sensor back so it is about 15 cm away from the edge of the coil.
Turn on Signal Generator #1. Start recording and slowly move the Magnetic Field Sensor
along the center of the track, keeping the probe parallel to the track, until the end of the
sensor is about 15 cm past the other edge of the coil. Then stop recording.
5. Explain the shape and magnitude of the plots of the parallel and perpendicular magnetic
fields.