In this experiment you will determine the direction of the B field surrounding a long straight wire using a compass, the induced voltage in a small inductor coil, and demonstrate the magnitude of the B field decreases as 1/r.

Lab@Home Box, 100mH inductor coil, small compass, and long straight wire apparatus.

When a current I exists in an infinitely long straight wire, the lines of magnetic induction B are concentric circles surrounding the wire. At a perpendicular distance r

 

from the wire, the B field is tangent to the circles as shown in Fig. 1. The direction of the current I is perpendicular to the plane of the page and directed out of the page. The direction of the current is by definition the direction that positive charge would flow. The magnitude of the B field as a function of I and r is given by where -7 weber/amp-m, I is in amperes, and r is in meters. The units of B are weber/m2 which has been given the name Tesla.

The direction of the B field relative to the current direction is given by the right hand rule.
If the current in the long straight wire is constant in time, the B field created by that current will be constant in time. For that case the direction of the B field can be determined by observing the effect of the B field on a small compass placed in the vicinity of the long straight wire. A portion of the laboratory will use a compass to investigate the direction of the B field in this manner.
If the current in the long straight wire is an alternating current produced by a sine wave generator, the B field surrounding the wire will also be time-varying, and it will alternate in direction and magnitude. If a small coil of self inductance 100 mH is placed next to the wire, an alternating voltage will be induced in the coil. According to Faraday's law of induction, this induced voltage in the coil is proportional to the rate of change of the magnetic flux through the coil, and hence to the magnitude of the time-varying B field.
Therefore, a measurement of the voltage induced in the coil, as the coil is placed at different distance from the wire, provides a relative measure of the magnitude of the B field at different distances from the wire. Note carefully that the quantity actually measured is an alternating electric voltage, but its magnitude is proportional to the B field and will be taken to be a relative measurement of the B field at a given point.

Experimental Procedure and Questions:

Part 1 Determination of the Direction of the B Field

1. Connect the circuit shown in Fig. 2 using the direct current power supply. Arrange the long wire apparatus so that the outside long wire is in a horizontal plane along a north-south axis. Ask your instructor the direction of north in the laboratory room. Arrange the wire so that the direction of the current is from north to south. Determine the direction of the current by tracing the wires from the (+) terminal of the power supply. Have the circuit approved by your instructor to assure that the current is in the proper direction.

2. Turn on the power supply.

3. Place the compass in the middle of the long wire section directly above the wire as close to the wire as possible. State the direction (north, south, north-east, etc.) that the compass needle points. Record your answer in Data Table 1.

4. Place the compass in the middle of the long wire section directly below the wire as close to the wire as possible. State the direction (north, south, east, north-east, etc.) that the compass needle points. Record your answer in Data Table 1.

5. Stand the long wire apparatus on its end so that the current in the outside long wire is vertically downward. Place the compass next to the wire at the four positions indicated by the open circles in the Fig. 5 in the Data Sheet Section. The represents the downward current viewed from above. In the open circles representing the four compass positions, draw an arrow showing the direction that the compass needle points.

Part 2 Determination of Magnitude of the B Field as a Function of Distance from the Wire

1. Connect the circuit shown in Fig. 3 using the long wire apparatus and the sine wave generator. Turn the generator to maximum amplitude. State the long wire apparatus on its end so that the outside long wire is vertical.

2. Connect the inductor coil to the oscilloscope. Place the inductor coil on the platform as shown in Fig. 4. The axis of the inductor coil should be perpendicular to an imaginary line (shown as the dotted line labeled 1 in the figure) which is perpendicular to the current-carrying wire. The inductor coil was shown in three different positions with the axis of the coil at different distance r1, r2, and r3 from the wire. At each position of the inductor coil shown the B field will alternate in opposite directions along the axis of the coil. The coil is chosen to be short ( 1 cm) and small cross-section (diameter 1 cm) because for that choice, the B field lies approximately along the coil axis and is approximately uniform over the cross-section of the coil.

3. The amplitude of the induced voltage on the oscilloscope will depend upon the frequency of the generator sine wave. With the inductor about 3 cm from the wire vary the frequency of the generator until the maximum voltage is read on the oscilloscope. Once this frequency at which the maximum voltage occurs is found, do steps 4-7 without changing the frequency. Make all measurements at this frequency.

4. Measure the voltage induced in the inductor coil as a function of r. The quantity r is the distance from the center of the coil to the center of the wire. Take data from r = 3.0 cm to r = 9.0 cm in increments of 1 cm. The reason that data is not taken for r less than 3 cm is the fact that at distances close to the wire, the B field is not even approximately uniform over the cross-section. Record the values of the voltage in the Data Table 2 under the column labeled B (trial 1). If this were a true measure of the B field, the units would be Tesla. Since the measured quantity is really a voltage which is proportional to B, no units are stated.

5. Repeat step 4 two more times measuring the induced voltage as a function of distance and recording the values in the Data Table 2 under Trial 2 and Trial 3.

6. Calculate the average B from trial 1, trial 2, and trial 3.

7. Make a graph of the data for B average verses 1/r to show the straight line.

8. Now measure the amplitude and frequency of the wave on the oscilloscope.* What is the origin of the signal? Compare the frequency of the induced signal to that provided by the generator. What happens to the amplitude and frequency of the signal when you change the frequency of the output wave?

9. What happens to the appearance of the signal when you change the knob marked “volts/div”? What happens to the amplitude and frequency of the signal? Is this what you expected? Explain.*

10. What happens to the appearance of the signal when you change the knob marked “sec/div”? What happens to the amplitude and frequency of the signal? Is this what you expected? Explain.*

11. The form for this lab report is attached to this handout. Fill in the tables, do the graph and calculations, and answer the questions in the space provided. Turn in both pages of the lab report when you leave today. You DO NOT have to turn in any additional reports on this lab next week so go enjoy the Spring weather!

*Refer to page 22 of the oscilloscope lab or ask your instructor if you need help to do this.


Name:
Section:
Lab Partner:

Lab Report: Magnetic Induction

Data and Calculations Tables(questions 1-6):
Data Table 1

With compass above wire compass direction =
With compass below wire compass direction =

Fig. 5 Indicate the compass direction at the positions shown.

Data Table 2

r (cm) BTrial 1 BTrial 2 BTrial 3 B(Average)
3.0
4.0
5.0
6.0
7.0
8.0

Graphs and Short Answer(questions 7-10):

7. Graph B vs. 1/r (you may attach an Excel graph)

8. Amplitude and frequency of generator and oscilloscope wave.

9. Explain what happens when you change the knob marked volts/div?

10. Explain what happens when you change the knob marked sec/div?