Lab 4-Magnetic Fields

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15 Lab 4: Magnetic Fields Introduction Magnetic fields are intrinsically connected to moving electric charges or electric currents. Faraday’s Law tells us that whenever an electric current flows through a wire, a magnetic field is produced in the region around the wire, linking the tenets of electricity and magnetism into one theory, called electromagnetism . Magnetic fields are vector fields, with a vector having both magnitude and direction describing the magnetic force which would be exerted at a particular point in space. When a magnetic field ( B ) is generated from the current ( I ) of a long, straight wire, the magnitude of the magnetic field located a distance r from the wire is given by the equation: where B is the magnetic field (in Tesla), μ 0 is the permeability of free space constant (= 4 π × 10 -7 T · m/A), I is the current, and r is the perpendicular distance from the wire to the point where the magnetic field is being measured. The direction of the field can be determined by the “right-hand rule” (Figure 4.1). You should refer to your text book for a description and a derivation of this formula from either the Biot-Savart Law or Ampere’s Law. Although the equation above gives the magnetic field in units of Tesla, the equipment in this experiment measures the magnetic field in units of “Gauss” (1 Gauss = 10 -4 Tesla). When current is run through the coils of a solenoid, a magnetic field is created inside the solenoid which runs along the central axis of the cylindrical shape. The magnetic field inside a solenoid which has a current I running through the coils is given by the equation: where n is the number of turns (coils) per unit length, and the direction of the field can again be determined by using the “right-hand rule”. A device which measures magnetic fields is referred to as a magnetometer , the most common type of which is a Hall probe . The Hall probe used in this experiment measures the magnitude of the magnetic field that is perpendicular to the probe and located at the small white oval at the end of the probe. The white oval thus indicates the sensitive region of the probe, and the signal which is sent to the computer is interpreted and displayed in the units of Gauss. 0 2 I B r μ π = v v Fig. 4.1: Diagram showing the “right-hand rule” for determining the direction of the magnetic field due to a line of current. 0 B nI μ = v
16 Experiment 1 – The Magnetic Field due to a Long Straight Wire In this experiment, the Hall probe will be used to measure the magnetic field generated by a specified current running through a straight wire. By measuring the field at varying radial distances from the wire, you will be able verify the equation described above and compare your measured values of B to the theoretical values of B determined using the equation. Procedure [1] Verify that the Hall probe amplifier is connected to the PASCO interface and that the switch on the amplifier is set to the “High Amplification (200x)” setting. Upon opening the “Magnetic Field” experiment file, a meter showing the magnetic field will be displayed on the computer screen. [2] The field due to the long straight wire is quite weak, and is comparable in strength to the Earth’s magnetic field and other stray magnetic fields. If you are having trouble getting meaningful measurement, try turning the sensor upside-down so that the white dot is pointing toward the board instead of straight up. [3] Connect the power supply and current meter to the long straight wire as shown in Figure 4.2, taking special care to connect the positive and negative wires correctly. [4] Turn on the power supply and adjust the current to 4 amps. Be careful not to exceed 4 amps. Record the value of the current. [5] Measure the magnetic field as near as possible to the wire (.005 m or .5 cm). When measuring the field, the probe should be held flat against the board with the white oval facing upward. Record your data in a table like the one below. [6] Repeat the above measurement moving outward in steps of 0.005 m (0.5 cm) until you reach a distance of 0.07 m (7 cm), recording the measurements in your data table. Analysis [1] Using the equation given in the introduction for the magnetic field due to a long straight wire, calculate the theoretical value of B for the distances measured above. [2] Calculate the percentage difference between the measured and theoretical values for three measurements (closest, farthest, and middle distances from the wire). Include the result in your data table. [3] Using a data analysis program, plot the measured value of the magnetic field on the vertical ( y ) axis, and the distance from the wire on the horizontal ( x ) axis. Fit the curve with an inverse ( 1 / r ) function. Does the data agree with the functional form of the equation for the magnetic field due to a long straight wire? Distance Measured B (Tesla) Theoretical B (Tesla) Percent Difference (%) 0.005 m 0.010 m … 0.070 m Table 5.1: Sample data table for magnetic fields data. Fig. 4.2: A schematic drawing showing the electrical connections for this experiment.
17 Experiment 2 – The Magnetic Field Inside a Solenoid This experiment will determine the magnetic field produced inside a solenoid and verify the equation described in the introduction. The solenoid in this experiment will be an extended metal Slinky ® , through which current will run in order to generate a magnetic field inside the coils. The magnetic field will be measured by inserting the Hall probe through the coils, and then compared to calculated theoretical values of the magnetic field due to a solenoid. Procedure [1] Verify that the Hall probe amplifier is connected to the PASCO interface and that the switch on the amplifier is set to the “High Amplification (200x)” setting. Upon opening the “Magnetic Field” experiment file, a meter showing the magnetic field will be displayed on the computer screen. [2] Stretch the Slinky ® to a length of 0.5 – 0.6 m (50-60 cm) on the meter stick. Try to keep the coils uniformly distributed over the central region, which is where the measurements will be made. [3] Using the wire clips provided, connect the power supply to the solenoid (through the current meter). Note and record the polarity of the connection to the solenoid. See Figure 4.3 for a description of the electrical connections. [4] Turn on the power supply and set the current to 2 amps. Do not exceed 2 amps. Record the value of the current for your lab report. [5] Insert the Hall probe into the center of the solenoid and measure the magnetic field at the center of the solenoid. Is the magnetic field reasonably constant over the interior cross-section of the solenoid? [6] Measure and record the magnetic field inside the coil for currents of 1.5, 1.0, and 0.5 amps. [7] In the region of the solenoid where the probe was inserted into the coil, count the number of complete turns (coils) in .1 m (10 cm) and record this value for your lab report. Analysis [1] Using a data analysis program, plot the measured value of the magnetic field on the vertical ( y ) axis, and the current in the solenoid on the horizontal ( x ) axis. Fit the curve with a linear function. Is the magnetic field directly proportional to the amount of current supplied? [2] Calculate the number of number of turns per meter for the region of the solenoid where the measurements were made. Use this value to calculate the theoretical value for the magnetic field in the solenoid using the equation described in the introduction for each of the four current settings. [3] For the four current values, calculate the percentage difference between the theoretical value and the measured value, and record all of this data in a data table similar to that from the previous experiment. Fig. 4.3: Photo showing the Slinky ® stretched along the meter stick, with the electrical connections to the power supply and current meter displayed.
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