You have a part time job working in a laboratory developing large liquid crystal displays that could be used for very thin TV screens and computer monitors. The alignment of the liquid crystals is very sensitive to magnetic fields. It is important that the material sample be in a fairly uniform magnetic field for some crystal alignment tests. The laboratory has two nearly identical large coils of wire mounted so that the distance between them equals their radii. You have been asked to determine the magnetic field between them to see if it is suitable for the test. You decide to make a graph of the field strength along the axis of the coils.
a. Draw a picture of the situation showing the direction of the current through each coil of wire. Establish a single convenient coordinate system for both coils. Label all of the relevant quantities.
b. Select a point along the axis of the two coils at which you will determine an equation for the magnetic field. To solve this problem, add the magnetic field from each coil at the selected point along the axis.The origin of your coordinate system for this problem cannot be at the center of both coils at once.
c. Use your equation to graph the magnetic field strength as a function of position from the common origin along the central axis of the coils. Describe the qualitative behavior of the magnetic field between the two coils. What about the region outside the coils?
