magnetic field of a straight wire.nb

Magnetic Field of a long straight wire using IO lab device.Christopher UbingCochise College

Abstract: Ampere’s law states that the magnetic field of a long straight wire is dependent on the dis-tance from the wire and the current going into the wire. We will first determine the current in the wire by means of measuring the magnetic field from the wire at a fixed distance. We will then take data at fixed distances from the wire to determine the distance dependance of the magnetic field generated by the current in the wire.

Equipment needed:1. IO device.2. 20 gauge wire (about a meter).3. Battery Holder (Single D cell should be fine).4. 30 cm Ruler5. Tape.6. Laptop computer with IO lab analysis software and spreadsheet software.7. (Optional) Single or Double Pole switch.

Theory:

The magnetic field in space around an electric current is proportional to the electric current which serves as it’s source. Ampere’s law states that for any closed loop path, the sum of the length elements times the magnetic field in the direction of the length element is equal to the permeability constant times the current enclosed in the loop. In the language of calculus.

B.dl = μ0 Ienc (1)

For the case of the long straight wire, we will create a circular path of radius r, around the wire, which simplifies the integral into the circumference of a circle

B.dl = B (2 π r)

Placing this result in equation (1) and solving for B, we get

2 π r B = μ0 Ienc

2 magnetic field of a straight wire.nb

B =μ0 Ienc2 π r (2)

In this experiment we want to examine the field strength vs distance away from a long copper wire. The challenge with this experiment, is that there is always a certain amount of magnetic field due to the field of the Earth. Since there is no way to shield our experiment from the Earth’s magnetic field, we will have to account for it in the data that we take. So, the first part of our procedure is to discover the magnetic field strength along the direction perpendicular to the wire without current. This quantity will be B0, and we will check to see if it changes as we move our sensor away from the wire. The second part of our experiment will be to ascertain the amount of current that is generated by the battery. We can do this by determining the magnetic field of the wire (current on) at a fixed distance from the wire. Note again, we will have to correct for the magnetic field of the Earth. Once we have a fixed current established, we will vary the distance of the sensor from the wire taking data at different distances from the wire and

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Fig 1: Experiment setup with all equipment needed to run the lab. Orient the remote so that the +z axis is facing towards the wire as shown.

Procedure 1. Determine Magnetic field of the Earth at your location.

Since we are interested in the magnetic field due to the wire, it is necessary to determine the back-ground magnetic field of your location. So, with the lab set up, we take magnetic field readings with no current flowing in the wire. Note, we are only interested in the magnetic field along the z axis of the device.

1. Connect dongle to computer.2. Turn on IO lab device and software.3. In the sensor list on the right hand side of the screen, select the Magnetometer.4. In the graph heading, uncheck the Bx components.5. In the smoothing menu, select smoothing to be 15.6. Without connecting the batteries to the wire, click record, and let it run for 5 seconds.

Record the average value of the z component of the magnetic field below. This will be your B0z. Do the same for the x component of the B field.

Keep in mind that this will be your baseline magnetic field that you will have to subtract out from your data.

Procedure 2. Determination of current.

In this part, you will obtain the magnetic field reading of the wire at a fixed distance from the wire. You can then use this current throughout the remainder of the experiment*.

1. Click the reset button on the software tool bar. This will clear your graph, but will also reselect Bx and By. Make sure that you uncheck them again before you begin. 2. Measure the length of the wire you have between the tape. You will place the IO lab device at a fixed distance from the center of the wire, as shown in figure 1. I Suggest that you place the device about 5 cm away from the wire.


1. Click the reset button on the software tool bar. This will clear your graph, but will also reselect Bx and By. Make sure that you uncheck them again before you begin. 2. Measure the length of the wire you have between the tape. You will place the IO lab device at a fixed distance from the center of the wire, as shown in figure 1. I Suggest that you place the device about 5 cm away from the wire.

L = ___ ___ ___(* lengh of wire between the tape. *)

3. Place the D battery in the holder. Using clip leads, connect the red line of the battery holder to the left hand side of the wire. Connect another clip lead to the right hand side of the wire but do not con-nect it right away to the black lead of the battery holder.

4. Click record, then connect the black lead of the battery holder to the wire. Let it run for a few sec-onds and disconnect. Stop the recording and using the analysis tools, determine the average magnetic field in the z direction for the time that the wire was connected to the battery

5. Click add run and repeat the process in step 4. Do this three times taking down the average back-ground field and the average magnetic field when the wire is connected to the battery.

6. Using Excel or your favorite spreadsheet program, create a four column data table with the following categories:

a) Distance from wire, (d)b) Measured magnetic field for both Bx and Bz. Units will be μTc) Background field (B0) for both x and z. Same units for b)d) Magnetic field from wire (Bz and Bx).

The last column, you can calculate the actual value of the magnetic field of the wire by subtracting the background field from the measured field. A sample for this part of the experiment is shown below.

Analysis:1. Find the average of the three trials for the magnetic field from the wire

2. Assuming equation (2) is true, determine the current being generated in the wire by connecting to the battery.

Procedure 3, Behavior of the field with distance.

In this last segment, we examine how the field behaves as we move the detector further away from the wire.

1. Using clip leads, connect the red line of the battery holder to the left hand side of the wire. Connect another clip lead to the right hand side of the wire but do not connect it right away to the black lead of the battery holder.

2. Set up the software to use the magnetometer, make sure that you uncheck By, and set the smooth-ing to 15. Move the remote 2 cm from the wire.

3. Click record, and connect the other end of the wire to the battery holder. Let the system record for about 10 sec and disconnect the other end of the wire from the battery holder after about 8 sec. You will have both components and the background field in your graph.

4. Click add run. Move the detector away from the wire by 2 cm to set up the next distance. Click record and reconnect the wire so that current is flowing. Record for another 10 seconds, disconnect the wire after 8 sec.

5. Repeat 3 and 4 for distances 6, 8, and 10 cm. You should then have a set of 5 values for both Bx and Bz.


In this last segment, we examine how the field behaves as we move the detector further away from the wire.

1. Using clip leads, connect the red line of the battery holder to the left hand side of the wire. Connect another clip lead to the right hand side of the wire but do not connect it right away to the black lead of the battery holder.

2. Set up the software to use the magnetometer, make sure that you uncheck By, and set the smooth-ing to 15. Move the remote 2 cm from the wire.

3. Click record, and connect the other end of the wire to the battery holder. Let the system record for about 10 sec and disconnect the other end of the wire from the battery holder after about 8 sec. You will have both components and the background field in your graph.

4. Click add run. Move the detector away from the wire by 2 cm to set up the next distance. Click record and reconnect the wire so that current is flowing. Record for another 10 seconds, disconnect the wire after 8 sec.

5. Repeat 3 and 4 for distances 6, 8, and 10 cm. You should then have a set of 5 values for both Bx and Bz.

Analysis of the data.

1. Create a spreadsheet with columns for the distance, measured field, background field and field due to the wire for both the x and z components. 1a) Comparing with the theoretical calculation, you will find that there is more than one component of the magnetic field changing. Why?2. Make a plot of the field vs 1/distance for both x and z components of the wire? Do both the x and z components obey Ampere’s law? You will likely see something very strange for the z component of the field for the wire? 3. What would happen to the field values if you reversed the current in the wire? 4. How would your data be affected if you were moving to the right of the wire instead of the left.5. Examine what the y component of the field looks like by rechecking the By field in the magnetome-ter. You will not need to run the experiment again, the IO lab will take the data for By even if you don’t want to see it. Why does it remain unchanged?


Appendix. Results from running the experiment.After 5 trials, our window in the analysis software looked like this. We will use these values for the data table and subsequent curve fit.

Note that the first run is the base field for both directions. We use this value throughout the data table given below to calculate the actual field due to the wire.

We created a table of the data in Logger Pro with the following results.

We created plots of both Bz and Bx vs distance in meters. These plots are shown below


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magnetic field of a straight wire.nb