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.
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