Magnetic Field Measurements Electromagnetism I. Introduction & Brief Description of the Concepts Magnetic field can be obtained naturally through a permanent or can be generated in the laboratory through a current carrying wire. In this laboratory, you will perform two activities: (1) measure and describe the strength of the magnetic field out of a permanent magnet, and (2) Measure the magnetic field strength obtained from a solenoid. The strength of a magnetic field from a permanent magnet varies inversely with the distance from the magnet similar to the electric and gravitational field strengths. But also, the strength of the magnetic field could vary in a different way relative to distance. The gravitational field of a point mass or the electric field of a point charge are both radial, while the magnetic field of a magnet consists of complete loops that surround and go through the magnet as shown in the figure below. Figure 1 In this lab, we will try to determine the equation of the magnetic field's strength at the vicinity the magnet's axis. You need to try to fit your results using this equation: B = a * d', where "d" is the distance between the sensor and the magnet, "a" and "b" are the coefficients of the fit. "b" is a value you need to determine experimentally from the best fit function to your data (b is expected to be negative, you can try different values for b for example 0, -0.5, -1, -1.5, -2, -2.5... etc). NOTE: there are formulae that can be used to calculate the field from a rectangular magnet but the formulae get too long and complex. Therefore, we are going to rely on the measurement to determine an empirical formula for themagnetic field strength of our rectangular magnets. Another way of obtaining a magnetic field, is to generate it ourselves. In fact, it was determined that a current carrying wire will eventually generate a magnetic field around the wire. This is an observation credited to the Danish Physicist and Chemist, Hans Christian Oersted. The generated magnetic field, have field lines located on a plane perpendicular to the current carrying wire and the magnitude of the filed varies with distance from the wire. This observation is taken to new levels, because of the need to use uniform magnetic field in some of the most interesting applications for example: the Magnetic Resonance Imaging (MRI) and also in Particle Physics Detectors. In this lab, we use a solenoid made of a length of wire wound around a cylinder, like string wound around a spool, forming several consecutive loops. This arrangement will provide a bigger magnitude for the magnetic field inside the solenoid. The field strength inside a solenoid is derived from Ampere's law. The magnitude of the field depends on the number of turns of wire per unit length: n=N/L, and on the current "I" in the wire, as follows: B = Ho * n * I, where Ho = 4m * 10 7T.m/A. In this lab, we measure the magnitude of the magnetic field at different distances, then we will determine the relationship between the measured strength of the magnetic field and the distance from the magnet. II. Lab Procedure, Data Taking and Preliminary Data Analysis 1. The APP needed is: https://phet.colorado.edu/en/simulation/legacy/magnets- and-electromagnets. 2. Permanent Bar Magnet and Electromagnet are used. 3. Three coils: coil "A" has I turn, coil "B" has 2 turns and coil "C" has 4 turns. a) Lab Procedure & Data Taking: Use the Magnetic Field Meter (Sensor) to measure the magnetic field strength of a permanent magnet as a function of the distance between the field meter and the magnet changes.Activity 1: Magnetic Field out of a Bar Magnet Lab Setup, Data Recording and Preliminary Analysis 1. Use the Bar Magnet simulation part of the Jar program (use 100% strength). 2. Place the Magnetic Field Meter at six different positions from the magnet. The six positions are marked in Figure 2, then fill Table 1. Bar Magnet Electromagnet PHET Bar Magnet Strength: 100 % 50 100 Flip Polarity N See Inside Magnet Show Field Magnetic (B) Field Show Compass 71.23 G Show Field Meter Bx 71 00 G Show planet Earth DV -5 80 G -4.67 0 Reset All Figure 2: Bar Magnet: we use the graph mesh to set the distance scale. Distance 1.25 2.25 |3.25 4.25 5.25 6.25 B (mT) Table 1: Note the distance variable has an arbitrary scale (unit). 3. Insert your data and plot the data for table 1 in the excel file I posted in the same folder "Magnet Bar" a. The fit function (trendline) will define the power (n) of the distance Bal/r"Activity 2: Magnetic Field out of a Solenoid Equipment Setup, Data Recording and Preliminary Analysis 1. Use the electromagnet simulation part of the Jar program. a. coil "A" has 1 turn, coil "B" has 2 turns and coil "C" has 4 turns 2. Set the voltage to 10 V, then position the field meter at the center of coil "A" to measure the maximum strength of the magnetic field: record this value in the table 2. 10 V 8V 6V 4V 2V OV Coil "A" Coil "B" Coil "C" Table 2: Magnetic Field Strength from Coils 3. Keeping the field meter in its fixed location, decrease the voltage from 10 V to 0.0 volts by 2 volts step and record the values of the maximum magnetic field strengths in the table 2. NOTE: changing the input voltage is the same as changing the input current, since current and voltage are directly proportional. 4. Replace coil "A" by coil "B" and then by coil "C", and in each case: measure the maximum field strength for different voltages, then record the values in the excel table 2.III. Post-Lab: Final Data Analysis and Conclusion 1. Activity (1): Based on the results of the curve fit, what is the relationship between the magnetic field strength and the distance from the magnet? 2. Activity (2): Describe the variation of the magnetic field strength as a function of: [create the corresponding graphs, using excel] a. B(N): The number of turns of each coil? b. B(I): The input current (remember: input current is directly proportional to the input voltage)? 5. We assume that the coils (A, B and C) have the same length: LA = LB = Lc= 1.67 mm and same resistance for each coil is R = 1ohm. Make the necessary calculations for every measurement for the magnetic field shown in (Table 2, Activity 2), and compare the calculations with the measurements, by specifying the accuracy of each measurement. a. Insert your data in Table 3 in excel file