2/4/2015 223 Physics Lab: Magnetic Force due to a Current-carrying Wire

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223 Physics Lab: Magnetic Force due to aCurrent­carrying Wire

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PurposeBackground MaterialExperimentObjectivesEquipment and SetupHints and Cautions

Online AssistanceLab ReportTemplateNudge QuestionsQuestionsTA Notes

Data, Results andGraphsAnswers to QuestionsLab ManualCUPOL Experiments

Purpose

The purpose of this lab experiment is to investigate the magnetic force of a current­carrying wire. Inthis experiment we will investigate the effects of current, length of wire and magnetic field strengthon the magnetic force.

Background

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

(1)

where , is the charge of the particle. If the angle between the particle's velocity vector and thedirection 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 right­hand 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 theupward direction, for both particles. However, from Equation 1 we see that the direction of themagnetic force depends on the charge of the particles. As Figures 2 and 3 show, the positivelycharged 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 downwarddeflection of the negatively charged particle.

 

2/4/2015 223 Physics Lab: Magnetic Force due to a Current-carrying Wire

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

 

     

 Figure 2. As shown in Figure 1, thispositively charged particle experiencesan upward magnetic force.

 Figure 3. As shown in Figure 1, thisnegatively charged particle experiences adownward 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 themagnetic field is , where is the wire's cross­sectional area and is the length of wire that isembedded within the magnetic field. If we define to be the number of charged particles per unitvolume, at any instant there are charges within that segment of wire. Therefore from Equation3, 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)

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

 

Figure 4. A representation of charged particles, with some drift velocity,  , flowingthrough a wire of which a portion of its length,  , is embedded in a uniform magneticfield,  . The wire has uniform cross­sectional area,  . When the charges passthrough uniform magnetic field they experience a magnetic force,  , as described inthe text. The total magnetic force on the wire is  , where   is the current inthe 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 magnetassembly, comprised of six removable horseshoe magnets, is placed on a triple­beam balance,and the balance is then zeroed. A variable current source is connected to the current balanceassembly, which has at one end a removable wire loop etched onto a circuit board. This wire loopis then placed into the permanent magnet assembly so the wire loop is perpendicular to themagnetic field but is not touching the magnets. Then, when a current flows through the wire loop, amagnetic force is created. Since the wire loop is stationary the magnetic force acts on thepermanent magnet assembly causing its weight to either increase or decrease depending on thedirection of the current and the orientation of the magnetic field. The change in the magnetassembly'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 passesthrough the circuit board wire loop. This force acts on the permanent magnet assembly

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causing a change in its weight. The change in the magnet assembly's weight is directlyproportional 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.)

As with all physics laboratory experiments, one must be careful to use the appropriate units. If allforces (i.e., the magnetic force and weight) are measured in newtons ( ), charges in coulombs (), and velocities in meters per second ( ), then from Equation 1 the unit of the magnetic field isgiven as newton per coulomb­meter per second. In SI units this is known as the tesla ( ) where

(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 100Surface of the Sun 0.01 100

Surface of Earth 0.5x10­4 0.5

Human brain 10­15 10­11

Footnotes

1. See Serway and Beichner, page 910.

Objectives

1. Use the magnetic force apparatus to verify that the magnetic force due to a current­carrying wire immersed in a perpendicular uniform magnetic field is proportional to each of

 

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the following parameters:A. length of the wireB. electrical current flowing in the wireC. magnitude of the magnetic field

Equipment and setup

(Figure 6.) The experimental setup. Note thecurrent in the wire is 2.26A.(Figure 7.) Permanent magnet assembly with sixhorseshoe magnets. Two of the horseshoemagnets are on the table top.(Figure 8.) Three of six interchangeable circuitboard wire loops. Notice the right­most wire loop isprinted on the front and back of the circuit board,effectively doubling the length of the wire shownon one side. Be careful when removing andinserting these somewhat fragile circuit boards.(Figure 9.) A close­up of a wire loop inserted intothe permanent magnetic assembly.(Figure 10.) The triple­beam balance.(Figure 11.) The variable current source. See theHints and Cautions section for instructions onproducing a constant current.(Figure 12.) Use the power supply's digitalammeter to measure the current.

Vernier caliperLab standBanana cords

[Click on images to enlarge.]

6 7

8 9

10 11

12    

Hints and Cautions

1. Caution!!! Do not touch the metal arms of the circuit board holder while current is flowingthrough 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 VOLTAGEADJUST knob fully clockwise, then adjust the DC CURRENT ADJUST knob to obtain the desiredoutput current.

Online Assistance

1. xxx2. Adding a trendline to an Excel plot3. Adding a non­linear trendline to an Excel plot4. Create plots of two data series on one graph5. Fitting multiple curves (trendlines) to one data set6. Clemson Physics Lab Tutorials7. Measurement uncertainties8. Using Excel9. Graphing data using Excel

2/4/2015 223 Physics Lab: Magnetic Force due to a Current-carrying Wire

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10. Using error bars in Excel

Lab Report Template

Each lab group should download the Lab Report Template and fill in the relevant information asyou perform the experiment. Each person in the group should print­out the Questions section andanswer them individually. Since each lab group will turn in an electronic copy of the lab report, besure to rename the lab report template file. The naming convention is as follows:

[Table Number][Short Experiment Name].doc.

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

Nudge Questions

These Nudge Questions are to be answered by your group and checked by your TA as you do thelab. 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 triple­beam balance to measure the magnetic force, ?8. Is it important that the triple­beam balance be properly zeroed before the experiment

begins? Why or why not?9. How will you insert the circuit­board 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?

Objective 1: Part A Nudges

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?

Objective 1: Part B Nudges

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?

Objective 1: Part C Nudges

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?

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5. What current value(s) will you use for this experiment? Remember not to exceed 5A!

Questions

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

Describe how your observations would change if the direction of the current were in the oppositedirection.

Describe how your observations would change if the permanent magnetic assembly wererotated 180° that is, if the direction of the magnetic field was in the opposite direction.

Show that it is only the horizontal portion of the circuit board wire that contributes to the verticalmagnetic force. In other words, show that the vertical portion of the wire does not vary the weightof the magnet assembly.

From your results in Part C, what can be said about the relative strengths of each horseshoemagnet?

What was the magnetic field strength of the permanent magnet assembly with all six horseshoemagnets installed? Is this a reasonable value?

From your observations of the triple­beam balance and the current readings, show that the redend of the horseshoe magnet is the "north" end.

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?

Is this experimental setup sensitive enough to measure the earth's magnetic field, ? If not, what

can be done to make this measurement possible?

TA Notes

This lab was designed as a one­week experiment. Expectations regarding the length andquality of the written lab report should be lowered. Essentially, students should work efficientlyand quickly to solve the Objectives, and succinctly report on their findings.

Store the magnets in pairs, with N poles attached to S poles!

Data, Results and Graphs

Enter TA password to view sample data and results of this experiment (MS Excel format):

Open

Lab Manual

Enter TA password to view the Lab Manual write up for this experiment (MS Word format):

Open

CUPOL Experiments

As of now, there are no CUPOL experiments associated with this experiment.

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If you have a question or comment, send an e­mail to Lab Coordiantor: Jerry Hester

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Photo's courtesy Corel Draw. Last Modified on 01/27/2006 14:25:18