Chapter 7. Magnetic Fields. 7.1 Purpose. 7.2 Introduction

Transcription

1 Chapter 7 Magnetic Fields 7.1 Purpose Magnetic fields are intrinsically connected to electric currents. Whenever a current flows through a wire, a magnetic field is produced in the region around the wire. The purpose of this lab is to investigate magnetic fields around simple geometric configurations of wires carrying current. 7.2 Introduction Note: For this experiment, you will write a complete (formal) lab report and hand it in at the next meeting of your lab section. This lab can not be your dropped grade for the semester. Magnetic fields are vector fields. A vector (direction and magnitude) describing the magnetic field can be associated with each point in space. The magnitude of the magnetic field from a long straight wire is: B = µ 0I 2 r (7.1) where B is the magnetic field in Tesla, µ 0 is the permeability of free space (4 x10 7 T m/a), Iisthecurrentandristheperpendiculardistancefromthewiretothepointwherethe magnetic field is being measured. The direction of the field is given by the right hand rule. (Refer to your text book for a description and a derivation of the formula from the Biot- Savart Law or Ampere s Law and Figure 7.1). Also note that a Tesla is a very large unit of magnetic field strength. Magnetic fields are also measured in units of Gauss which are equal to 10 4 Tesla. The apparatus used in this experiment displays magnetic fields in Tesla. The magnetic field inside of a solenoid is given by: B = µ o ni (7.2) 41

2 Figure 7.1: Right hand rule. Figure 7.2: Closeup of the Hall probes at the end of the sensor. where n is the number of turns (coils) per unit length and I is the current. The direction of the field is given by the right hand rule. Adevicewhichmeasuresmagneticfieldsiscalledamagnetometer. Onecommontype of magnetometer is a Hall probe. The senor used in this experiment has two Hall probe devices mounted perpendicularly to one another at the end of the clear plastic probe end of the sensor. The position of each Hall probe sensor is indicated by a white dot at the end of the clear plastic probe body. See Figure 7.2. A switch on the body of the sensor indicates which Hall probe is used. There is also a switch for the range and a tare (zero) button. The Hall probe used in this experiment displays readings in units of Tesla. 7.3 Procedure Long Straight Wire Special Cautions: Do not exceed 5 amps on the long straight wire or 4 amps on the solenoid. Do not disconnect or break the long straight wire. 42

3 + + Amp Meter Power Supply o Long Straight Wire o Hall Probe Figure 7.3: Schematic diagram (left) and photograph (right) of the long straight wire setup. Because the magnetic field of the earth is approximately the same size as the field produced by the long straight wire, it is important to align the long straight wire in a direction where there is minimal interference from the earth s magnetic field. It is also critical to zero the Hall probe carefully when measuring the magnetic fields. In addition, the magnetic field decreases rapidly from the wire so careful measurement of the small distances are required for accurate results. The apparatus consists of a long wire on a board. Current is supplied by a power supply through an ammeter. The ammeter must be set to the 10 Ampere scale. A schematic and photograph of the apparatus is shown in Figure 7.3. Open the file magnetic field. A meter showing magnetic field and a graph of magnetic field strength vs. time will be displayed on the computer screen. Verify the range select switch is set to 100X and the Hall probe is set to Radial (towards the clear plastic probe end). Verify the power supply is properly connected to the long wire and the ammeter is connected properly on the 10 Ampere setting. Place the board so the wire is parallel to the compass needle. Place the Hall probe sensor on the board with the white dot facing up and the body of the Hall probe sensor perpendicular to the wire. Place the center of the white dot on the Hall probe 1 cm (0.01 m) from the wire. Start Capstone and push the TARE button on the hall probe. probe. Do not move the Slowly increase the current until the ammeter reads 5 Amperes. Since the meter reading may fluctuate, highlight the region on the magnetic field vs. time graph with the most constant (flat) value. The statistic value for the mean is the best value for the magnetic field. Record the current, the magnetic field including the sign, and the distance of the Hall probe from the wire. 43

4 Turn o the current and move the Hall probe to 1.5 cm (0.015 m) from the wire. Zero the probe using the TARE button. Increase the current back to 5 Amperes. Record the current, the magnetic field including the sign, and the distance of the Hall probe from the wire as before. Repeat the procedure for distance values of 2.0 cm, 2.5 cm, 3.0 cm and 3.5 cm with the current at 5 Amperes. Plot the data with magnetic field on the y-axis and position from the wire on the x- axis. Plot the expected values for the magnetic field at the appropriate distances from the wire from Equation 7.1. How do the calculated values compare to the measured values? Calculate the percentage di erence for the magnetic field for each distance from the wire. Using the right hand rule, explain why the sign of the field is correct. The magnetic field of the earth is about the same magnitude as the field measured near the long straight wire. Why could we ignore this field in our measurement? Solenoid Special Cautions: Do not bend or distort the coils of the slinky. Do not exceed 4 Amperes through the coil. A metal stretched-out slinky will provide a reasonable helical coil of wire (solenoid) to generate a solenoidal magnetic field. The field is constant inside the coil away from the ends. Remove the power supply connections to the long straight wire. The same file ( magnetic field) will be used for this part of the experiment. The Hall probe selection and range select switches should remain the same as in the first part of the experiment. Remove the banana wires from the long straight wire board. Stretch the slinky 60 cm to 70 cm ( m) on the meter stick. See Figure 7.4. Make sure the coils of the slinky are uniformly distributed over the central region where the measurements will be made. Using the alligator clips at each end of the slinky, connect the banana leads from the power supply through the ammeter to each end of the slinky. Note and record the polarity of the connection to the solenoid. Place the meter stick and solenoid (slinky) so the compass needle points perpendicularly to the solenoid. In the middle region of the slinky where the probe will be inserted, count the number of complete turns (coils) in.25 m (25 cm). Calculate the number of turns per meter and record the value. 44

5 Figure 7.4: The solenoid (slinky) stretched along the meter stick used in the second part of the experiment. With the current in the coil at zero Amperes, insert the Hall probe into the center of the middle region of the solenoid through the side of the slinky. (The body of the probe should be perpendicular to the axis of the solenoid.) Zero (tare) the sensor. Turn on the power supply and set the current to 4 amperes. Do not exceed 4 Amperes. Measure the magnetic field at the center of the solenoid. Record the current and magnetic field. Is the magnetic field reasonably constant over the interior cross-section of the solenoid? Repeat the above procedure with currents of 3.0, 2.0 and 1.0 Amperes in the coil. Make a plot with the magnetic field on the vertical axis and the current on the horizontal axis. Does the magnetic field increase linearly with current? Do the magnitude and direction of the magnetic field agree with the value calculated from Equation 7.2? Calculate the percentage di erence between the calculated values of the magnetic field and the measured values for each value of the current. Why is the field larger with the solenoid than with the straight wire? 45

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