lec10a - Scott Hughes Massachusetts Institute of Technology...

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Scott Hughes 11 March 2005 Massachusetts Institute of Technology Department of Physics 8.022 Spring 2004 Lecture 10: Addendum Clarification to the magnetic field of a sheet 10.7 Field of a plane of current, revisited The geometry of the vectors that are needed to understand the magnetic field produced by a sheet of current is kind of grotty. A lot of people were somewhat befuddled at the end of the March 10 lecture. To clarify things, I present here some more detailed versions of the figure that appeared in Lecture 10; hopefully, this will help lay out why the magnetic field is (a) purely horizontal and (b) depends on the cosine of the angle in the figure. Here is the sheet. In this figure, I’ve squished all the wires down into a nice, thin sheet. Consider the contribution to the magnetic field arising from a “chunk” of current to the right of the midpoint: L x θ y rhat φ hat The radial direction from that chunk of current points along the red ˆ r vector that I’ve drawn.
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