Lab 5 Magnetic Fields



Lab 8: The Earth’s Magnetic Field

Preliminary Questions

1. A coil (n = 10 loops) is connected in series with a power supply and a variable resistor, as shown in the figure below. The coil has a radius of 10 cm (0.10 m) and is oriented so that it is perpendicular to the Earth’s Magnetic field (i.e. due east or west).

a. When the current in the circuit is 0.5 amps, what is the magnetic field magnitude at the center of the coil due to the current? Refer to the equation below…

b. A compass is placed at the center of the coil and reads 46o east of north when current is running through the circuit. What the magnitude of the total magnetic field at the center of the coil? Note: the compass points due north when there is no current in the circuit.

c. Based on this information, what is the magnitude of the Earth’s magnetic field? Note: this calculation will yield only the horizontal component of the Earth’s magnetic field.

d. A dip angle is used to determine the angle of the Earth’s magnetic field above the horizon and measures an angle of 68o above the horizon. Based on your information above and this measurement, what is the total magnitude of the Earth’s magnetic field?

Part A Magnetic Field Mapping

1. Use a compass to map the magnetic field of a magnet placed on a piece of paper. Make sure that other magnets on your table are not near enough to disturb the results.

2. Now place two bar magnets end to end (North to South), and sketch the resulting magnetic field. Does it look like you expected it to?

3. As a result of what you observed in steps 1 and 2, sketch (to scale) the magnetic field that you would expect to find surrounding half of a bar magnet.

Part B The Earth’s Magnetic Field

In the previous exercise, you used the deflection of a compass to determine the magnetic field around various objects. If this compass were held far from any magnetic objects, it would point North due to the fact that the earth itself acts like a huge magnet. Today we will determine the value of the earth’s magnetic field by comparing it to the magnetic field created at the center of a circular current carrying loop.

(Actually, you would have to go outside, far from any buildings to get an accurate value for the earth’s magnetic field. Do this if you would like, or else note that the magnetic field you are measuring is actually the one present at your table due to the earth as well as other influences in this building.)

For a circular loop, the magnetic field at the center is given by

[pic]

where (0= 1.26x10-6 T.m/A, N is the # of loops, i is the current in the loop, and R is the radius of the loop. When there are N loops, each one contributes this amount, and so the total magnetic field at the center is given by.

1) Connect a Current Probe to Ch1 of the LabPro interface. Then start the LoggerPro software and the “EarthsMagneticField” experiment file.

2) Click on the LabPro icon and select Ch4. Set it to Analog out then select the waveform to “DC Output” and click on the “Create User Parameters”.

3) Set the compass inside the loop, and arrange it so that the compass needle lies in the plane of the loop when no current is running through it. Try to set this up as far as possible from other magnetic objects.

4) Now, without moving the loop, attach it to a series circuit containing the LabPro Analog Out leads, a 10 Ω resistor, and a current probe.

5) You can alter the current in your circuit by changing amplitude value of Analog Out. Try several different amplitudes and notice the changing deflection of the compass needle. When the needle is deflected, it is responding to the additional magnetic field created by the current carrying loop. The total magnetic field acting on the compass is now the vector sum of this new field (Bcoil) and the horizontal component of the earth’s magnetic field (Bearth).

6) Collect measurements of i and the angle of deflection (() of the compass needle using LoggerPro.

7) For even better data, reverse the current at each voltage amplitude (i.e. switch the leads to the power supply) and take a measurement of the current and compass deflection in the opposite direction.

8) Repeat steps 6 and 7 for four different voltage amplitudes so that you have 5 values of Bcoil and a total of 10 data points! It’s a good idea to record the measurement values in the data table below.

9) Create calculated columns in LoggerPro for Bcoil and tan (.

|( (o) |i (A) |N |tan ( |Bcoil(T) |

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|Slope of Graph | |Uncertainty of Slope | | |

10) Create a graph of Plot Bcoil vs. tan(() and fit the graph to an appropriate function (should be linear). Record the slope of the fit and its uncertainty in the above table.

Analysis:

1. From the vector diagram below, it is apparent that there is a direct relationship between Bearth and Bcoil that relates directly to the graph you constructed above. How are Bearth and Bcoil related? Express this relationship in terms of Bcoil= …

2. What is the significance of the slope of your graph in terms of your response to the previous question?

3. One last thing: The earth’s magnetic field does not lie exactly in the plane of the compass. The value for Bearth that we have obtained is only the horizontal the component of the earth’s magnetic field in that direction.

To determine the actual direction of the earth’s magnetic field, place the “dip” needle along the direction of the earth’s magnetic field (you may want to take this measurement outside). The angle that is read off the side is the dip angle ((), or angle of declination. We can use this angle to determine the total magnitude of the earth’s magnetic field:

θdip = _______________

4. Based on your results above, determine the magnitude of the Earth’s magnetic field with an estimate of the uncertainty.

5. Compare your answer with the textbook (or instructor) and estimate the experimental error of your measurement.

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Current Probe

R=10Ω

Analog Out

A

Coil

(n = 10 loops)

+

-

θ

Bearth horizontal

Bearth tot

Bearth vertical

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