PASCO scientific Science Workshop

Vol. 2

Physics Lab Manual: P53 - 1 Magnetic Field of Helmholtz Coils

Experiment P53: Magnetic Field of Helmholtz Coils (Magnetic Field Sensor, Power Amplifier) Concept magnetism

Time SW Interface Macintosh File 45 m 700 P53 Mag. Field Helmholtz

EQUIPMENT NEEDED • Science Workshop™ Interface • Magnetic Field Sensor • Power Amplifier • (2) Helmholtz coils

• • •

Windows File P53_HELM.SWS

(2) Laboratory Jacks meter stick, wooden (3) Patch Cords

PURPOSE The purpose of this laboratory activity is to examine the magnetic field produced by the current in a pair of Helmholtz coils, and to measure the magnetic field strength between the coils and compare the measured value to the theoretical value. THEORY Helmholtz coils are a pair of coils that each have the same radius, R. The coils are placed parallel to each other a distance R apart and along the same axis. The magnetic field along the axis at the midpoint between the two coils is then given by B=

8µ o NI 125R

where µo = 4π x 10-7 (tesla•meters)/amp, I is the current (amps) in one coil, R is the radius of the coil, and N is the number of turns of wire in one coil. PROCEDURE In this activity, the Power Amplifier supplies the current through the Helmholtz coils. The Magnetic Field Sensor measures the strength of the magnetic field between the coils. You will type in the value for the position of the sensor as you move it along the axis of the two coils. The Science Workshop program controls the Power Amplifier and measures and displays the strength of the magnetic field and the position of the sensor. You will compare the measured magnetic field strength to the theoretical magnetic field strength.

jhn

©1996, PASCO scientific

P53 - 1

P53 - 2: Physics Lab Manual Magnetic Field of Helmholtz Coils

Vol. 2

PASCO scientific Science Workshop

PART I: Computer Setup 1.

Connect the Science Workshop interface to the computer, turn on the interface, and turn on the computer.

2.

Connect the Magnetic Field Sensor DIN plug to Analog Channel A on the interface.

3.

Connect the Power Amplifier to Analog Channel B. Plug the power cord into the back of the Power Amplifier and connect the power cord to an appropriate electrical receptacle.

4.

Open the Science Workshop document titled as shown: Macintosh P53 Mag. Field Helmholtz

•

The document opens with a Digits display of magnetic field strength, a Digits display of current, and a Graph display of Field Strength vs. Position. It also has the Signal Generator window that controls the Power Amplifier.

•

Note: For quick reference, see the Experiment Notes window. To bring a display to the top, click on its window or select the name of the display from the list at the end of the Display menu. Change the Experiment Setup window by clicking on the Zoom box or the Restore button in the upper right hand corner of that window.

P53 - 2

Windows P53_HELM.SWS

©1996, PASCO scientific

jhn

PASCO scientific Science Workshop

Vol. 2

Physics Lab Manual: P53 - 3 Magnetic Field of Helmholtz Coils

5.

The Signal Generator is set to output DC at 10.0 V. It is set to Auto so it will start automatically when you click MON or REC and stop automatically when you click STOP or PAUSE.

6.

The Sampling Options… are: Periodic Samples = Fast at 10 Hz, and Keyboard with Parameter = Position and Units = m.

7.

Arrange the windows so you can see the Digits display for Current and the Digits display for Magnetic Field Strength.

PART II: Sensor Calibration & Equipment Setup •

You do not need to calibrate the Magnetic Field Sensor or the Power Amplifier. The Magnetic Field Sensor produces a voltage that is directly proportional to the magnetic field strength as follows: 10 millivolts = 10 gauss (where 1000 gauss = 0.1 tesla). The sensor’s range is ±2000 gauss. However, you should increase the sensitivity of the Magnetic Field Sensor.

1.

Change the Experiment Setup window from REDUCED SIZE to FULL SIZE by clicking on the Zoom box or the Maximize button.

FULL SIZE

ZOOM BOX

CLOSE BOX

MACINTOSH®

jhn

©1996, PASCO scientific

MINIMIZE RESTORE BUTTON BUTTON

CONTROLMAXIMIZE MENU BUTTON BUTTON

REDUCED SIZE

WINDOWS®

P53 - 3

P53 - 4: Physics Lab Manual Magnetic Field of Helmholtz Coils

2.

In the Experiment Setup window, doubleclick the Magnetic Field Sensor icon to open the Sensor Setup window.

3.

In the Sensor Setup window, click on Sensitivity: and select Med (10x) from the menu. Click OK to return to the Experiment Setup window.

4.

In the Experiment Setup window, click on the Zoom box or the Restore button to return the window to its reduced size.

P53 - 4

Vol. 2

©1996, PASCO scientific

PASCO scientific Science Workshop

jhn

PASCO scientific Science Workshop

Vol. 2

Physics Lab Manual: P53 - 5 Magnetic Field of Helmholtz Coils

Equipment Setup 1.

Connect the Helmholtz coils in series with the output from the Power Amplifier. Use one patch cord to connect the positive terminal of the Power Amplifier to the positive terminal on the first coil. Use a second patch cord to connect the negative terminal on the first coil to the positive terminal on the second coil. Use the third patch cord to connect the negative terminal on the second coil to the negative terminal on the Power Amplifier. (TOP VIEW)

+

–

COILS

+

POWER CORD

POSITIVE TERMINAL POWER AMPLIFIER

–

NEGATIVE TERMINAL

TO INTERFACE

2.

Measure the radius of a coil. Record the radius in the Data section. Position the two coils so they are one radius, R, apart and parallel to each other.

3.

Construct a guide for the Magnetic Field Sensor in the following way: Place a laboratory jack on each side of the Helmholtz coils to support the meter stick. Place the meter stick through the Helmholtz coils as shown with the 50 cm mark of the meter stick at the midpoint between the coils.

4.

Adjust the position of the laboratory jacks so they are at least 30 cm from the center of the coils.

5.

Adjust the height of the laboratory jacks so the Magnetic Field Sensor can move along the center line (vertically) of the two coils when it rests on the meter stick. Make sure the meter stick is level.

jhn

©1996, PASCO scientific

P53 - 5

P53 - 6: Physics Lab Manual Magnetic Field of Helmholtz Coils

PASCO scientific Science Workshop

Vol. 2

TO INTERFACE

R

MAGNETIC FIELD SENSOR

COILS CENTER LINE METER STICK LAB JACK

POWER AMPLIFIER

PART III: Data Recording 1.

Hold the Magnetic Field Sensor away from any magnetic field sources. Zero the sensor by clicking the ZERO button on the top of the sensor bos.

2.

Select the AXIAL field by clicking the FIELD SELECTOR SWITCH on the top of the Magnetic Field Sensor.

3.

AXIAL RADIAL ZERO

Place the sensor box on top of the meter stick with the end of the sensor rod aligned with the 30 cm mark, facing toward the coils. Hold the sensor in place.

FIELD SELECTOR SWITCH ZERO BUTTON

MAGNETIC FIELD SENSOR

4.

Turn on the power switch on the back of the Power Amplifier.

•

Note: The red light-emitting diode (LED) on the front of the Power Amplifier may light up. This indicates that the Power Amplifier is providing maximum current.

P53 - 6

©1996, PASCO scientific

jhn

PASCO scientific Science Workshop

Vol. 2

5.

Click the REC button ( ) to begin collecting data. The Keyboard Sampling window will open. Move the Keyboard Sampling window so you can also see the Digits display of Current and the Digits display of Magnetic Field Strength.

6.

Record the value shown in the Digits display for Current in the Data section.

•

The Keyboard Sampling window shows the parameter and units above the Data list. The default value for Entry #1 is 10.0000.

7.

With the end of the sensor at the 30 cm mark, type in -20 as Entry #1*. Click Enter to record your typed in value.

•

Your typed in value for Entry #1 appears in the Data list.

Physics Lab Manual: P53 - 7 Magnetic Field of Helmholtz Coils

*Entry #1 is -20 because the sensor is 20 centimeters from the center of the coils.

8.

Move the end of the sensor from 30 cm to 35 cm, or five centimeters closer to the center of the coils. Type in -15 as Entry #2 in the Keyboard Sampling window. Click Enter to record your typed in value.

•

After you click Enter, your second typed in value appears as #2 in the Data list. The default value for Entry #3 changes to reflect the pattern of your first two entries.

jhn

©1996, PASCO scientific

P53 - 7

P53 - 8: Physics Lab Manual Magnetic Field of Helmholtz Coils

Vol. 2

9.

Move the end of the sensor from 35 cm to 40 cm, another five centimeters closer to the center of the coils. Because the default value in the Keyboard Sampling window is -10.0000, click Enter to record this value as Entry #3.

•

The third entry appears in the Data list and the default value changes to -5.0000 in the Keyboard Sampling window.

PASCO scientific Science Workshop

NOTE: You will now move the sensor through the coils by one centimeter increments. 10.

Move the end of the sensor from 40 cm to 41 cm (or one centimeter closer to the center of the coils). Type in -9 for Entry #4 and click Enter to record your value.

•

Your typed in value appears as #4 in the Data list. The default value changes to reflect the new pattern.

11.

Move the end of the sensor from 41 cm to 42 cm. Because the default value is already -8.0000, click Enter to record it.

12.

Continue to move the end of the sensor by one centimeter increments through the middle region of the coils. Click Enter to record each new position.

13.

When you reach the 60 cm mark on the meter stick, change the position of the end of the sensor by five centimeters (or from 60 cm to 65 cm.) Click Enter to record the value.

14.

Move from 65 cm to 70 cm for the last measurement. When the sensor is at the 70 cm mark, click Enter to record the value.

15.

Click the Stop Sampling button in the Keyboard Sampling window to stop collecting data.

•

The Keyboard Sampling window will disappear, and Run #1 will appear in the Data List in the Experiment Setup window.

16.

Turn off the Power Amplifier.

P53 - 8

©1996, PASCO scientific

jhn

PASCO scientific Science Workshop

Vol. 2

Physics Lab Manual: P53 - 9 Magnetic Field of Helmholtz Coils

ANALYZING THE DATA ) to rescale the

1.

Click the graph display to make it active. Click the Autoscale button ( graph to fit the data.

2.

Click the Smart Cursor button (

•

The cursor changes to a cross-hair shape when the cursor is in the display area of the graph. Move the cursor to the position that corresponds to the midpoint between the coils. The Ycoordinate of this point is displayed along the Y-axis. The X-coordinate of this point is displayed below the X-axis.

•

Record the magnetic field strength (Y-coordinate) for the midpoint between the coils.

3.

Record the number of turns in one of the coils.

4.

Calculate the theoretical value of the magnetic field at the midpoint between the Helmholtz coils using the measured current, radius, and number of turns for the coil.

5.

Compare the theoretical value to the measured value at the midpoint using a percent difference.

).

DATA Item

Value

Radius of coil

m

Number of turns Current

A

Measured field strength

gauss

Theoretical field strength

gauss

Percent difference

%

QUESTIONS 1.

Based on your graph, over what distance along the axis can the magnetic field be considered a constant?

2.

How did the measured value of magnetic field strength compare to the theoretical value? What factors may have caused the difference, if any?

jhn

©1996, PASCO scientific

P53 - 9

P53 - 10: Physics Lab Manual Magnetic Field of Helmholtz Coils

Vol. 2

PASCO scientific Science Workshop

OPTIONAL •

Hold the Magnetic Field Sensor in your hand. Click MON to monitor data. Use the sensor to explore the entire volume between the two coils. Pay attention to how much variation there is in the field as the sensor is moved away from the center.

•

If it is possible to change the separation between the coils, repeat the experiment with the coils separated by 1.5 R instead of R.

OPTIONAL QUESTIONS 1.

How uniform is the magnetic field between the coils as the sensor was moved radially outward from the center toward the windings of the coils?

2.

If a different separation of the coils was used, how did that affect the answers to the first two questions?

P53 - 10

©1996, PASCO scientific

jhn