Exhibit: table of content

Mathematics Maths21a, Summer 2005
Multivariable Calculus
Oliver Knill, SciCtr 434, knill.harvard.edu
The animation shows the "dynamo". One of the laws in electromagnetism links magnetic field B and electric field E by
d/dt B = c curl(E),
where c is the speed of light. If we look at the flux of both sides throught the surface spanned by the wire, we obtain on the left hand side the rate of change of the magnetic flux and on the right hand side using Stokes the line integral of c E along the wire. This line integral is a voltage. By turning the wire, the flux of the magnetic field changes. This produces an alternating voltage: the work done by turning the wire generates electricity.
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Oliver Knill, Maths21a, Multivariable Calculus, Summer 2005, Department of Mathematics, Faculty of Art and Sciences, Harvard University