Chapter 7

Magnetic Fields

7.1 Purpose

Magnetic fields are intrinsically connected to electric currents. Whenever a current flowsthrough a wire, a magnetic field is produced in the region around the wire. The purposeof this lab is to investigate magnetic fields around simple geometric configurations of wirescarrying current.

7.2 Introduction

Note: For this experiment, you will write a complete (formal) lab report andhand it in at the next meeting of your lab section. This lab can not be yourdropped grade for the semester.

Magnetic fields are vector fields. A vector (direction and magnitude) describing themagnetic field can be associated with each point in space.

The magnitude of the magnetic field from a long straight wire is:

B =µ0I

2⇡r(7.1)

where B is the magnetic field in Tesla, µ0 is the permeability of free space (4⇡x10�7T ·m/A),I is the current and r is the perpendicular distance from the wire to the point where themagnetic field is being measured. The direction of the field is given by the right hand rule.(Refer to your text book for a description and a derivation of the formula from the Biot-Savart Law or Ampere’s Law and Figure 7.1). Also note that a Tesla is a very large unitof magnetic field strength. Magnetic fields are also measured in units of ’Gauss’ which areequal to 10�4 Tesla. The apparatus used in this experiment displays magnetic fields in Tesla.

The magnetic field inside of a solenoid is given by:

B = µo

nI (7.2)

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Figure 7.1: Right hand rule.

Figure 7.2: Closeup of the Hall probes at the end of the sensor.

where n is the number of turns (coils) per unit length and I is the current. The directionof the field is given by the right hand rule.

A device which measures magnetic fields is called a magnetometer. One common typeof magnetometer is a Hall probe. The senor used in this experiment has two Hall probedevices mounted perpendicularly to one another at the end of the clear plastic probe end ofthe sensor. The position of each Hall probe sensor is indicated by a white dot at the end ofthe clear plastic probe body. See Figure 7.2.

A switch on the body of the sensor indicates which Hall probe is used. There is alsoa switch for the range and a tare (zero) button. The Hall probe used in this experimentdisplays readings in units of Tesla.

7.3 Procedure

7.3.1 Long Straight Wire

Special Cautions:

• Do not exceed 5 amps on the long straight wire or 4 amps on the solenoid.

• Do not disconnect or break the long straight wire.

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Power

Supply

oo

Ha

ll P

ro

be

Meter

Amp

+ −− +

Long Straight Wire

Figure 7.3: Schematic diagram (left) and photograph (right) of the long straight wire setup.

Because the magnetic field of the earth is approximately the same size as the field pro-duced by the long straight wire, it is important to align the long straight wire in a directionwhere there is minimal interference from the earth’s magnetic field. It is also critical to zerothe Hall probe carefully when measuring the magnetic fields. In addition, the magnetic fielddecreases rapidly from the wire so careful measurement of the small distances are requiredfor accurate results.

The apparatus consists of a long wire on a board. Current is supplied by a power supplythrough an ammeter. The ammeter must be set to the 10 Ampere scale. A schematic andphotograph of the apparatus is shown in Figure 7.3.

• Open the file ’magnetic field’. A meter showing magnetic field and a graph of magneticfield strength vs. time will be displayed on the computer screen.

• Verify the ’range select’ switch is set to ’100X’ and the Hall probe is set to ’Radial’(towards the clear plastic probe end). Verify the power supply is properly connectedto the long wire and the ammeter is connected properly on the 10 Ampere setting.

• Place the board so the wire is parallel to the compass needle.

• Place the Hall probe sensor on the board with the white dot facing up and the bodyof the Hall probe sensor perpendicular to the wire. Place the center of the white doton the Hall probe 1 cm (0.01 m) from the wire.

• Start Capstone and push the ’TARE’ button on the hall probe. Do not move theprobe.

• Slowly increase the current until the ammeter reads 5 Amperes.

• Since the meter reading may fluctuate, highlight the region on the magnetic field vs.time graph with the most constant (flat) value. The statistic value for the ’mean’ isthe best value for the magnetic field.

• Record the current, the magnetic field including the sign, and the distance of the Hallprobe from the wire.

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• Turn o↵ the current and move the Hall probe to 1.5 cm (0.015 m) from the wire. Zerothe probe using the ’TARE’ button. Increase the current back to 5 Amperes. Recordthe current, the magnetic field including the sign, and the distance of the Hall probefrom the wire as before.

• Repeat the procedure for distance values of 2.0 cm, 2.5 cm, 3.0 cm and 3.5 cm withthe current at 5 Amperes.

• Plot the data with magnetic field on the y-axis and position from the wire on the x-axis. Plot the expected values for the magnetic field at the appropriate distances fromthe wire from Equation 7.1. How do the calculated values compare to the measuredvalues? Calculate the percentage di↵erence for the magnetic field for each distancefrom the wire.

• Using the right hand rule, explain why the sign of the field is correct.

• The magnetic field of the earth is about the same magnitude as the field measurednear the long straight wire. Why could we ignore this field in our measurement?

7.3.2 Solenoid

Special Cautions:

• Do not bend or distort the coils of the slinky.

• Do not exceed 4 Amperes through the coil.

A metal stretched-out slinky will provide a reasonable helical coil of wire (solenoid) togenerate a solenoidal magnetic field. The field is constant inside the coil away from the ends.

• Remove the power supply connections to the long straight wire.

• The same file (’magnetic field) will be used for this part of the experiment. The Hallprobe selection and range select switches should remain the same as in the first partof the experiment. Remove the banana wires from the long straight wire board.

• Stretch the slinky 60 cm to 70 cm (0.6 - 0.7 m) on the meter stick. See Figure 7.4.Make sure the coils of the slinky are uniformly distributed over the central region wherethe measurements will be made.

• Using the alligator clips at each end of the slinky, connect the banana leads from thepower supply through the ammeter to each end of the slinky. Note and record thepolarity of the connection to the solenoid.

• Place the meter stick and solenoid (slinky) so the compass needle points perpendic-ularly to the solenoid. In the middle region of the slinky where the probe will beinserted, count the number of complete turns (coils) in .25 m (25 cm). Calculate thenumber of turns per meter and record the value.

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Figure 7.4: The solenoid (slinky) stretched along the meter stick used in the second part ofthe experiment.

• With the current in the coil at zero Amperes, insert the Hall probe into the centerof the middle region of the solenoid through the side of the slinky. (The body of theprobe should be perpendicular to the axis of the solenoid.) Zero (tare) the sensor.

• Turn on the power supply and set the current to 4 amperes. Do not exceed 4Amperes. Measure the magnetic field at the center of the solenoid. Record thecurrent and magnetic field. Is the magnetic field reasonably constant over the interiorcross-section of the solenoid?

• Repeat the above procedure with currents of 3.0, 2.0 and 1.0 Amperes in the coil.

• Make a plot with the magnetic field on the vertical axis and the current on the hori-zontal axis. Does the magnetic field increase linearly with current?

• Do the magnitude and direction of the magnetic field agree with the value calculatedfrom Equation 7.2? Calculate the percentage di↵erence between the calculated valuesof the magnetic field and the measured values for each value of the current. Why isthe field larger with the solenoid than with the straight wire?

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