The Line Integral
The integral sign with a little circle means that we are integrating, or summing, around a closed curve. The shape of the curve is arbitrary, but it must coincide with the perimeter of the area used in computing the magnetic flux. In Faraday's law we are summing the induced electric field, so we must imagine, for each little element of length, dl, taking the dot product of the electric field vector at the element with the element of length itself.In the movie, the electric field is shown at several points around each of several circles. If you look carefully, you'll notice that the field is larger on the larger circles than on the smaller circles. This is because the larger circles enclose more magnetic flux.
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