The Northern Lights (aurora borealis) overMalmesjaur lake in Moskosel, Lappland, Swe-den. Image by Jerry MagnuM Porsbjer, re-leased under the Creative Commons license.http://www.magnumphoto.se

MAGNETIC FIELDSAND FORCES

Physics 241/261

Winter 2013

1 IntroductionJust as stationary electric charges produce electric fields, moving charges (currents) give rise to mag-

netic fields. In this lab you will investigate the magnetic field (denoted by ~B) produced by differentarrangements of currents and from a fixed bar magnet. You will use a sensitive force-measuring apparatusto study the right hand rule and the force on current-carrying wire. You will then study the right handrule of fields generated by current-carrying wires. Finally, you will measure the strength and properties ofmagnetic fields due to bar magnets and two different coil configurations.

2 TheoryBefore starting this lab, you should be familiar with the following physical concepts. If you need to

review them, or if you haven’t yet discussed them in your lecture course, consult the indicated sections inYoung & Freedman, University Physics.

• Magnetic fields and field lines, §27.2-3

• Magnetic Force on a Current Carrying Conductor, §27.6

• Magnetic field due to current in a circular loop, §28.5

• Ampere’s law, magnetic field due to a solenoid, §28.6-7 (Example 28.9)

2.1 UnitsThe SI unit for magnetic field is the Tesla (T). The Tesla is named after the eccentric but brilliant sci-

entist Nikola Tesla, who developed many of the magnetic devices used to generate and use AC (alternatingcurrent) electrical power on a large scale.

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One Tesla is equivalent to 10,000 gauss, where the gauss is an earlier unit that is still in common usage.Since the Tesla is a very large unit, corresponding to an unusually strong field, it is more common to useunits of millitesla (mT) or gauss (G),

1G = 10−4 T = 10−6 NA · cm

(1)

For example, the Earth’s field is about 0.5 G. The gaussmeter that you will use in this experiment alsomeasures in gauss.

2.2 Current Carrying WiresThe basic relationship for force on a charged particle traveling in a magnetic field is known as the

Lorentz force, given in Equation 2.~F = q~v×~B (2)

If we have a conductor of length L inside a magnetic field, we can relate the current in that wire to thevelocity of the charged particles traveling through the wire. Since v = L/t

I =qt=

qL/v

=qvL

(3)

By plugging q~v =~IL into Equation 2 we arrive at the relationship for the force on a current carrying wirein a magnetic field.

~F =~IL×~B = ILBsinθ (4)

In this equation, θ refers to the angle between the wire and the magnetic field. Since we take a crossproduct between the direction of current and the direction of the magnetic field, the direction of the forceis determined by the right hand rule. If you point your thumb in the direction of the current and yourfingers in the direction of the magnetic field, your fingers will curl into the direction of the force.

We also know that moving charges generate magnetic fields. The direction of this magnetic field isgiven by the right hand rule. Point your thumb in the direction of the current and your fingers will coil inthe direction of the magnetic field. So the field magnetic field lines from a wire form closed loops aroundthe wire. From Maxwell’s Equations, the strength of the magnetic field, B, at some distance, r, from awire carrying current, I, is described by

Bwire =µ0I2πr

(5)

µ0 = 4π ·10−7T ·m/A

2.3 Magnetic Fields of CoilsIf we curve a wire into a coil and pass a current through it, we can build larger fields than a simple wire

alone would produce. This is because in the center of this coil the field generated from each part of thewire points in the same direction. Since the fields are in the same direction, they add to produce a largerfield. Along the axis of this coil, the strength of the field is given by

Bcoil(z) =µ0NR2I

2(R2 + z2)3/2 (6)

In this equation, B(z) is the strength of the magnetic field. N is the number of turns of the coil. R is theradius of the coil. I is the current. z is the distance from the observation point to the center of the coil. The

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direction of the magnetic field is given by the right hand rule. If you wrap your fingers in the direction ofthe current, your thumb will point in the direction of the magnetic field.

Equation 6 assumed that the coil is infinitely thin. While this cannot be achieved in practice, it is oftena very good approximation. Another way of making a coil is to have a long coil, often referred to as asolenoid. In this case, the magnetic field inside the coil is constant. The direction is given by the sameright hand rule as thin coils. However the magnitude is now

Bsolenoid =µ0NI

L(7)

In this equation, N is the number of turns of the solenoid, I is the current, and L is the length.

3 Equipment• Bar magnet

• Goldstar power supply

• Goldstar DM332 digital multimeter, set for high-current measurements (10A maximum)

• Compasses

• DC Gaussmeter

• Oersted Table

• Amp-O-Matic power supply

• Electromagnet coil (TEL502 or equivalent)

• Stand for electromagnet coil

• Slinky solenoid and mounting board with hooks

• Probe stands for solenoid and Helmholtz coils measurements

• Magnetic Force Balance Table

• Digital Pocket Scale (Jennings JS-50x or similar)

• Rotating magnet stand

3.1 Magnetic Field Sensor (Gaussmeter)The device used to measure magnetic fields is traditionally called a “gaussmeter” (for reasons ex-

plained in Section 2.1). The magnetic field is a vector quantity, so it is characterized by a magnitude anda direction at any point in space. While a compass is only sensitive to the direction of ~B, the gaussmeteris sensitive to both its magnitude and direction. The sensitive area of the probe is a small spot located afew mm from the end of the probe tip, marked with a white dot. The probe measures ~B · n̂, where n̂ is thenormal vector into the end of the meter. That is, it measures the component of the magnetic field that isperpendicular and going into the probe face. This is illustrated in Figure 1.

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B

B

Zero Field ReadingMaximum Field Reading

Sensitive Spot

Ruler Ruler

Figure 1: Measuring the magnetic field using the gaussmeter.

In this experiment, you will use the 1999.9 G or “ON" setting on the gaussmeter (depending on model).When using the meter, it is important to “zero" your meter before most measurements. To do this, considerthe field you are trying to measure. Then, align the probe such that you expect that field not to interfere(e.g., turn the meter so that it is perpendicular to the field, or remove it from the area in which the fieldexists) . Then adjust the zero-adjustment knob until your meter reads between 0.0G and 0.3G. You mightneed to do this between successive measurements, even if for the same configuration of ~B fields. Any timeyou move the meter, you must re-zero it, since the local magnetic field can vary significantly in the room.You can expect up to a 0.3 G fluctuation in the reading. You should keep this uncertainty in mind whendoing your experiments.

3.2 Goldstar Power SupplyBeginning in Section 7, we will be using Goldstar power supplies as the mechanism for producing

currents and voltages to drive our experiments. The knobs on the front of these power supplies serve twopurposes: (1) limiting the current output, and (2) limiting the voltage difference between the two leads. Ifyou find that you are not able to achieve high enough currents, adjust the voltage knob to a higher voltage.If you cannot achieve a high enough voltage, adjust the current limiter knob. Ask your GSI if you havequestions about your power supplies.

3.3 Amp-O-Matic Power SupplyIn Section 6, we will use another power supply which has been specially configured to give currents

in the 5-10 A range. The Amp-O-Matic is shown, along with the Oersted table apparatus, in Figure 6. TheAmp-O-Matic’s operation is simple. Toggle the device with the ON/OFF switch. Also, notice that there aretwo banana jacks with which you can connect the Oersted table’s straight wire. Finally, there is a buttonwhich closes the circuit. When this button is pressed, current will flow out of the jacks, provided there isa circuit between them. Be sure to turn the Amp-O-Matic to OFF when not using the device.

4 Experiment: Magnetic Force on a Current Carrying WireYou will investigate how the force experienced by a current-carrying wire in a magnetic field depends

on the current in the wire and the angle between the current and the field. The apparatus you will use isfragile, and designed to be operated with minimal adjustment. Do not disassemble the apparatus after theexperiment. If your setup does not look like that in Figure 4, ask your GSI for assistance.

This device consists of a digital pocket scale, a pair of strong permanent magnets arranged to producea roughly constant field, and a short segment of wire. The magnets can rotate on a small turntable. Makesure that the wire does not touch the magnets and that it is in the center of the gap. If the wire is touchingthe magnet, DO NOT try to adjust the wires themselves. Instead, gently slide the magnet stand until the

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Figure 2: Gaussmeter.

?

?

Geographic north pole

Geographic south pole

Figure 3: The earth is a magnetic dipole.

Figure 4: Setup to study the force on a current-carrying wire.

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Figure 5: The magnetic field between the magnets points from one magnet to another, toward the “N" onthe compass. The poles of the magnets are on the faces rather than at the ends like you would normallyexpect of a bar magnet. The resulting magnetic field between the magnets of this configuration looks muchlike the electric field of a parallel plate capacitor.

wires are no longer touching the magnet. If you aren’t sure what to do, ask your GSI for assistance. Turnon the scale and zero it using the button on the lower right corner. Set the dial on the magnet stand to be at90◦, re-zeroing the scale if neccessary. Turn on the power supply and adjust the current to 0.5 A as read onthe ammeter and record the force (in grams) on the scale. You may notice that the wire moves when thepower supply is turned on and off. Measure the force as a function of the current for values of 0.5-2.5 Aat 0.5 A increments. Be sure to re-zero the scale between each measurement with the power supply turnedoff.

Graph your force vs. current data. Based on your graph, what can you conclude about the relationshipbetween force and current? That is, is the relationship linear, quadratic, exponential, inverse, etc?

Does your graph agree with theory?With the power supply off, set the dial on the scale to 45◦. Make sure that the wire does not touch the

magnets and that it is in the center of the gap. Re-zero the scale, turn the power supply on, and adjust thecurrent to 2.0 A. Record the force on the scale.

What is the ratio of the force on your wire at 45◦ to 90◦? What should the ratio be?Using equation 4 and your data at 90◦, estimate the magnetic field strength between the magnets.

Remember you will need to convert the force reading in grams into Newtons using F = mg, where g =9.8m/s.

5 Experiment: Field of a Bar MagnetThis exploratory part of the experiment is intended to help you familiarize yourself with the gaussme-

ter. While holding the North pole of the bar magnet near the gaussmeter, rotate the bar magnet until youget a maximum reading on the gaussmeter. Record the maximum magnetic field you measure as well asthe orientation of the magnet with respect to the detector end of the gaussmeter. Now try rotating the barmagnet until you can read as close to zero as possible, keeping it close to the North pole of the magnet.

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Again, record the magnitude and orientation.When these two measurements were performed, the gaussmeter was in the same magnetic field, since

it was in the same location relative to the bar magnet. Why does the orientation of the magnet with respectto the gaussmeter change the measured magnetic field?

You can think of the Earth’s magnetic field as being generated by a bar magnet. How would this barmagnet be oriented? That is, which magnetic pole of the bar magnet would lie near the geographic northpole?

6 Experiment: Magnetic Field Near a Current-Carrying Wire

Figure 6: Oersted apparatus to study the magnetic field of a straight wire.

Connect the Amp-O-Matic to the Oersted apparatus shown in Figure 6. We use the Amp-O-Matic sinceit can provide a larger current (about 5-10 A) than our power supplies, and we need a large current toproduce a measurable magnetic field. Arrange four small compasses at equidistant points around the wireon the stand. Record your observations of the compasses on your worksheet. Why are the compass needlesoriented the way they are when the battery is disconnected?

Press the red button on the front of the apparatus to complete the circuit and note the change in thecompass needles. WARNING: Do not leave the switch closed for more than a few seconds. This will makethe wires extremely hot. Be sure to note which way the compass needles move, and what happens whenthe current is turned on and off. What happens to the compasses when there is current in the wire? Applythe “right hand rule" to the system. Which direction do you expect the field to point? Do your observationsagree with this expectation?

Reverse the leads on the Amp-O-Matic and again note the change in the compasses. What was theeffect of reversing the leads?

Now that you know the direction of the magnetic field due to the wire, measure the magnetic field 1 cmaway from the wire. While one partner holds the gauss meter in the correct location, the other should zerothe meter (to eliminate the field of the room) and then press the red button on the power supply. Record

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Figure 7: Setup for measuring the magnetic field of a coil.

your measurement of the magnetic field and use it to calculate the current in the wire. Is your answerreasonable?

7 Experiment: Magnetic Field of a CoilPlace one N = 320 turn coils in the coil stand. With the power supply turned off and the current knob

turned all the way down, connect the coil in series with the ammeter and the power supply. Mount theprobe on the probe stand and position it 5 cm from the center of the coil, on the axis of the coil.

Turn on the power supply and adjust the current to 0.5 A as measured on the ammeter. Measure themagnetic field strength along the axis at z =−5,−2.5,0,2.5, and 5 cm along the axis of the coil, where 0is taken as the center of the coil.

From Equation 6, the magnetic field should be symmetric about the origin, B(z) = B(−z). Does yourdata support this prediction?

Use Equation 6 to calculate the expected field at z = 0,2.5, and 5 cm. How well does your data agreewith this calculation?

8 Experiment: Magnetic Field of a Slinky SolenoidA solenoid is a very long coil of wire. We will use a Slinky to investigate how the magnetic field of

a solenoid is different from the magnetic field of a typical coil, and how the magnetic field is affected byvarious factors.

Using the board and hooks, stretch the Slinky to 1.0 m in length (the distance between holes on theboard is 25 cm) and lock it in place. Connect the power supply to the Slinky using alligator leads (SeeFigure 8). Turn on the power supply and adjust the current to 2.0 A. Using the gaussmeter, measure the

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Figure 8: You can study the magnetic field of a solenoid using a Slinky and the gaussmeter.

magnetic field at various points along the axis of the solenoid. Take care to re-zero your gaussmeter beforeeach measurement to ensure the most accurate readings.

Is the magnetic field within your solenoid constant, to within the precision of the meter?About inside the end of the solenoid does the field reach its constant value?

9 Questions• Compare the magnetic field from the bar magnets in the force balance apparatus, the coils, and the

solenoid. Which gives you the strongest magnetic field?

• For conducting experiments and building devices, it is useful to have a controllable source of mag-netic fields. Which satisfies these requirements better, the bar magnets or coils?

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