The purpose of this lab experiment is to investigate the magnetic force of a current-carrying wire. In this experiment we will investigate the effects of current, length of wire and magnetic field strength on the magnetic force.

If a charged particle moves with some velocity, , through a uniform magnetic field, , it experiences a magnetic force given by

(1)

where , is the charge of the particle. If the angle between the particle's velocity vector and the direction of the magnetic field is , the magnitude of the magnetic force may be rewritten as

(2)

The direction of the magnetic force vector may then be found with the familiar right-hand rule. Notice that the magnitude of the force is a maximum when and is identically zero when .

Figure 1 shows two charged particles entering a uniform magnetic field . The velocity vector of each particle is given as , indicating that both velocity vectors are perpendicular to the direction of the magnetic field. Therefore the quantity becomes , or in the upward direction, for both particles. However, from Equation 1 we see that the direction of the magnetic force depends on the charge of the particles. As Figures 2 and 3 show, the positively charged particle experiences an upward force, , while the negatively charged particle experiences a downward force, . The manifestation of these magnetic forces is shown in Figure 1 by the upward deflection of the positively charged particle and the downward deflection of the negatively charged particle.

Figure 1. Two charged particles travel with some velocity, , through a uniform magnetic field, . As the charges pass through the magnetic field, each experiences a magnetic force, , due to their velocity, the direction and strength of the magnetic field and their charge, . Note that here the positive charge experiences an upward magnetic force and the negative charge experiences a downward force.

	Figure 2. As shown in Figure 1, this positively charged particle experiences an upward magnetic force.		Figure 3. As shown in Figure 1, this negatively charged particle experiences a downward magnetic force.

Figure 4 shows a segment of wire carrying a current that is located within a uniform magnetic field, . The force on each charged particle is given by

(3)

where is the drift velocity of the charged particles. The volume of the wire that exists within the magnetic field is , where is the wire's cross-sectional area and is the length of wire that is embedded within the magnetic field. If we define to be the number of charged particles per unit volume, at any instant there are charges within that segment of wire. Therefore from Equation 3, we can write the magnetic force on a wire of length as

(4)

Since the current flowing in a conductor is given as ¹, the above equation becomes

(5)

where is the vector length of wire that points in the direction of the current . Note that the direction of the current is defined as the direction in which positive charges move.

Figure 4. A representation of charged particles, with some drift velocity, , flowing through a wire of which a portion of its length, , is embedded in a uniform magnetic field, . The wire has uniform cross-sectional area, . When the charges pass through uniform magnetic field they experience a magnetic force, , as described in the text. The total magnetic force on the wire is , where is the current in the wire. Here , where is the number of particles with charge, .

Our experimental setup is shown in Figure 5 and is described as follows. A permanent magnet assembly, comprised of six removable horseshoe magnets, is placed on a triple-beam balance, and the balance is then zeroed. A variable current source is connected to the current balance assembly, which has at one end a removable wire loop etched onto a circuit board. This wire loop is then placed into the permanent magnet assembly so the wire loop is perpendicular to the magnetic field but is not touching the magnets. Then, when a current flows through the wire loop, a magnetic force is created. Since the wire loop is stationary the magnetic force acts on the permanent magnet assembly causing its weight to either increase or decrease depending on the direction of the current and the orientation of the magnetic field. The change in the magnet assembly's weight is due to the magnetic force given by Equation 5.

Figure 5. The experimental setup. A magnetic force is created when a current passes through the circuit board wire loop. This force acts on the permanent magnet assembly causing a change in its weight. The change in the magnet assembly's weight is directly proportional to the magnetic force.

Three parameters may be altered in this experiment, and they are as follows:

1. The length of wire may be varied by exchanging one wire loop for another.
2. The current amplitude may be varied by adjusting the output from the power supply. (The direction of the current flow may also be altered.)
3. The strength of the magnetic field may be altered by varying the number of horseshoe magnets in the magnet assembly. (The direction of the magnetic field may also be altered.)

(6)

If the current flow is measured in amperes (), then the tesla unit can be shown to be

(7)

It should be noted that magnetic field strength is often given in units of the gauss (), where . Table 1 shows magnetic field strengths of various bodies given in units of tesla and gauss.

Table 1

Magnetic Field Strengths of Various Bodies
Field Source	Field Strength (T)	Field Strength (G)
Superconducting magnet	30	3x105
Strong demonstration magnet	2	2x104
Medical MRI unit	1.5	1.5x104
Typical bar magnet	0.01	100
Surface of the Sun	0.01	100
Surface of Earth	0.5x10-4	0.5
Human brain	10-15	10-11

Footnotes

1. See Serway and Beichner, page 910.

1. Use the magnetic force apparatus to verify that the magnetic force due to a current-carrying wire immersed in a perpendicular uniform magnetic field is proportional to each of the following parameters:
   1. length of the wire
   2. electrical current flowing in the wire
   3. magnitude of the magnetic field

(Figure 6.) The experimental setup. Note the current in the wire is 2.26A. (Figure 7.) Permanent magnet assembly with six horseshoe magnets. Two of the horseshoe magnets are on the table top. (Figure 8.) Three of six interchangeable circuit board wire loops. Notice the right-most wire loop is printed on the front and back of the circuit board, effectively doubling the length of the wire shown on one side. Be careful when removing and inserting these somewhat fragile circuit boards. (Figure 9.) A close-up of a wire loop inserted into the permanent magnetic assembly. (Figure 10.) The triple-beam balance. (Figure 11.) The variable current source. See the Hints and Cautions section for instructions on producing a constant current. (Figure 12.) Use the power supply's digital ammeter to measure the current. Vernier caliper Lab stand Banana cords

[Click on images to enlarge.] 6 7 8 9 10 11 12

1. Caution!!! Do not touch the metal arms of the circuit board holder while current is flowing through them!

2. Caution!!! Be careful with the small etched circuit boards when inserting and removing them -- they can break easily!

3. Caution!!! Keep the current below 5A throughout the experiment!

4. The power supply should be set to constant current mode. To do so, turn the DC VOLTAGE ADJUST knob fully clockwise, then adjust the DC CURRENT ADJUST knob to obtain the desired output current.

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Each lab group should download the Lab Report Template and fill in the relevant information as you perform the experiment. Each person in the group should print-out the Questions section and answer them individually. Since each lab group will turn in an electronic copy of the lab report, be sure to rename the lab report template file. The naming convention is as follows:

For example the group at lab table #5 working on the Ideal Gas Law experiment would rename their template file as "5 Gas Law.doc".

These Nudge Questions are to be answered by your group and checked by your TA as you do the lab. They should be answered in your lab notebook.

General Nudges

1. How will you verify that the magnetic force is proportional to each parameter.
2. How many "experiments" must you perform to verify the relationship ?
3. What is the direction of ?
4. What is the direction of the current, or ?
5. In this experiment, what should the relationship be between the direction of and ?
6. What is the direction of relative to the directions of and ?
7. How will you use the triple-beam balance to measure the magnetic force, ?
8. Is it important that the triple-beam balance be properly zeroed before the experiment begins? Why or why not?
9. How will you insert the circuit-board wire loops into the permanent magnet assembly? Is the orientation and position of the wire relative to the magnets important?
10. How did you measure the length of the wire? Did you measure the entire length of the conductor?

1. For this part, which experimental parameters will you hold constant and which will you vary?
2. Which length(s) of wire will you use for this experiment?
3. How many magnets will you use for this experiment? Why?
4. What current value(s) will you use for this experiment? Remember not to exceed 5A!
5. What is the magnitude of the magnetic field used in this experiment?

1. For this part, which experimental parameters will you hold constant and which will you vary?
2. Which length(s) of wire will you use for this experiment? Why?
3. How many magnets will you use for this experiment? Why?
4. What current value(s) will you use for this experiment? Remember not to exceed 5A!
5. What is the magnitude of the magnetic field used in this experiment?
6. How does the magnetic field strength in this experiment compare to that of Part 1?

1. For this part, which experimental parameters will you hold constant and which will you vary?
2. Which length(s) of wire will you use for this experiment? Why?
3. Does the wire length affect the results?
4. How many magnets will you use for this experiment? Why?
5. What current value(s) will you use for this experiment? Remember not to exceed 5A!

These Questions are also found in the lab write-up template. They must be answered by each individual of the group. This is not a team activity. Each person should attach their own copy to the lab report just prior to handing in the lab to your TA.

Estimate the maximum possible magnetic force contributed by the earth's magnetic field, , to these experiments. Assume exists in the plane parallel to the earth's surface. What can be done with the experimental apparatus to eliminate this contribution?