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Unformatted text preview: timeter in the Equipment appendix. Read the section Measuring Constant Magnetic Field in the Software appendix. Read the appendices Significant Figures, Review of Graphs and Accuracy, Precision and Uncertainty to help you take data effectively. 149 DETERMINING THE MAGNETIC FIELD OF A COIL – 1302Lab5Prob5 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. WARM UP 1. Make a sketch of a coil of radius R. Define a coordinate axis, label the relevant quantities, and indicate the direction of the current through the coil. Select a point along the axis at which you will calculate the magnetic field. 2. Select a small element of current along the coil, which will cause a small fraction of this magnetic field. Label the length of that current element. Draw a position vector from that current element to the selected point along the axis of the coil. Use the Biot-Savart law to draw a vector representing the direction of the small part of the magnetic field from your current element at the position of interest. Determine the components of this vector along the axes of your coordinate system. Are there any symmetries that allow you to neglect one or more components of the magnetic field at the point of interest? 3. Use the Biot-Savart law to calculate the small part of the desired component of the magnetic field, at the selected point, from the small element of current. Now add up (using an integral) all of the small fractions of that component of the magnetic field from all of the small elements of current around the coil. Determine the magnitude of the magnetic field at that point along the axis for one loop of wire, writing your answer as a function of the distance along the axis of the coil. What will be the effect of N identical loops on the magnitude of the magnetic field? 4. Graph the magnitude of magnetic field strength as a function of the position along the central axis of the coil of wire. PREDICTION Calculate the magnitude of the magnetic field as a function of the position along the central axis of a coil of known radius, the number of turns of wire, and the electric current in the coil. Use this expression to graph the magnetic field strength as a function of position along the central axis of the coil. EXPLORATION 150 DETERMINING THE MAGNETIC FIELD OF A COIL – 1302Lab5Prob5 If you have the data from Measuring The Magnetic Field of One Coil you do not necessarily need to make any additional measurements. Go directly to the analysis section. If you have not done this, continue with the exploration. WARNING: You will be working with equipment that generates large electric voltages. 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. Never grasp a wire by its metal ends. Connect a large coil to the power supply using the adjustable voltage. Using your compass, make a qualitative map of the magnetic field produced. To get the most obvious effect on the compass, should the central axis of the coil be oriented N-S or EW? Decide whether you should set the amplifier to high or low sensitivity. Using your compass as an indicator, adjust the current up and down to determine the sensitivity of the magnetic field to the current. For a reasonable current in the coil, use the compass to determine how far a measurable magnetic field along the axis of the coil extends. Also check out the magnetic field outside the coil. Is it large or small? Compared to what? Try reversing the current through the coil. What happens to the magnetic field at each point? Connect the Hall probe as explained in the Equipment and Software appendices. Before you push any buttons on the computer, locate the magnetic field strength window. You will notice that even when the probe is held away from obvious sources of magnetic fields, such as your bar magnets, you see a non-zero reading. From its behavior determine if this is caused by a real magnetic field or is an electronics artifact or both? If you notice an ambient field, can you determine its cause? Go through the Hall probe calibration procedure outlined in the appendix, or in the Magnetlab Guide Box in the upper right corner of the application. Be sure the sensor amplification switch on the Hall probe is set to 6.4mT range. The MagnetLab application requires the probe to be set to the 6.4mT range to work correctly. Does the Hall probe ever read a zero field? Explore the strength of the magnetic field in the plane of the coil. Is the field stronger inside or outside the coil? Where is the field the strongest inside the coil? How far from the center of the coil along the axis can you measure the field? Is it the same on both sides of the coil? 151 DETERMINING THE MAGNETIC FIELD OF A COIL – 1302Lab5Prob5 How can you tell by your magnetic field reading if you are on the axis? How far from the axis can you move the Ha...
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