Choose a coordinate system on the small coil 2 use

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Unformatted text preview: geTimeLAB - MEASURING TIME-VARYING VOLTAGES and Measuring Constant Magnetic Field in the Software appendix. If equipment is missing or broken, submit a problem report by sending an email to labhelp@physics.umn.edu. Include the room number and brief description of the problem. 185 THE GENERATOR – 1302Lab6Prob5 WARM UP 1. Draw a picture of the equipment labeling the direction of the magnetic field and the orientation of the small coil. Choose a coordinate system on the small coil. 2. Use Faraday’s Law to relate the changing magnetic flux through the coil to the potential difference across the ends of the coil of wire. The changing magnetic flux is caused by the angular speed of the coil. 3. Draw a diagram showing only the small coil, a vector giving the direction of the magnetic field, and the area vector for the coil. 4. Write an equation for the magnetic flux through the small coil when it is stationary and at some angle to the magnetic field. As the small coil is rotated, how does the angle its area vector makes with the magnetic field vary with time? That variation is related to its angular speed. 5. Write an expression for the change in magnetic flux through the small coil as it turns. PREDICTION Calculate the potential difference produced by a coil of wire spinning in a uniform magnetic field as a function of its angular speed. EXPLORATION WARNING: You will be working with equipment that generates large electric currents. Improper use can cause painful burns. To avoid danger, the power should be turned OFF and you should WAIT at least one minute before any wires are disconnected from or connected to the power supply. You will want the largest magnetic field you can produce safely with the equipment. Develop a plan for measuring the magnetic field using the Hall probe and Magnetlab application. Where will you want to measure the magnetic field? Over what region do you need the magnetic field to be reasonably constant? Check to see if it is. Disconnect the Hall probe from the interface and plug in the voltage, attaching the clips to the ends of the small coil. The ends of the small coil are wired to the terminals on opposite ends of the axle about which the coil spins. Use the VoltageTime application to get an on-screen display of the small coil's potential difference versus time. With the Helmholtz coils generating a magnetic field, align the small coil such that its area vector is parallel to that magnetic field. What does the display of potential 186 THE GENERATOR – 1302Lab6Prob5 difference versus time read? Is this what you expected? Repeat by rotating the small coil so the area vector is perpendicular to the field. Now connect the motor to a power supply and note the appearance of the potential difference versus time display. Determine how you will measure the rotational period of and the potential difference across the small coil. How can you determine the angular speed of the coil from its rotational period? Try changing the motor’s speed by increasing the voltage applied to it. How does changing the speed affect the display? Determine the range of potential differences and rotational periods that you will use for your measurements so that you can set the scale for your graph of maximum potential difference as a function of rotational period. MEASUREMENT Note that the area of the small coil enclosed by the inner loops of wire is smaller than that enclosed by the outer loops of wire. Decide how to determine the effective area for the coil. Be sure to record in your journal how you found the effective area; think carefully about how you do this. Decide where you place the Hall probe to measure the magnetic field produced by the Helmholtz coils. Calibrate the probe at the point of interest with the power supply off. Measure the strength of the magnetic field, produced in the region of interest by the Helmholtz coils, using the Hall Probe. From the computer display of potential difference as a function of time, measure the maximum potential difference induced in the small coil and the rotational period of the small coil. If you have not done so, read the Software appendix that details how to use the VoltageTimeLAB application. Do several trials, rotating the coil at a different constant speed for each. How can you check your computer display to ensure that the coil is rotating at constant speed? ANALYSIS Determine the equation that best represents your collected data. What physical quantities do the constants in your equation represent? What do the variables in your equation represent? 187 THE GENERATOR – 1302Lab6Prob5 CONCLUSION What is the potential difference induced in a coil spinning in a uniform magnetic field? Did your measured potential difference agree with the predicted potential difference? Did the period of the signal agree with your predictions? If not, why not? What are the limitations on the accuracy of your measurements and analysis? How does the amount of potential difference produced by the generator depend on the angular speed at whi...
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