Problems for
Intermediate Methods in Theoretical Physics

Edward F. Redish

Line Integral for a Non-Conservative Loop

In a plasma, for a short time, the electric field is well described by the function

where C is a constant.   This field arises from both charges and from changing magnetic fields, so we cannot assume that there is a well-defined potential function for E .  

(a) Evaluate  

around the loop shown at the right for the given electric field by doing the line integrals explicitly.

(b) If we were to carry a charge, q , around the loop shown in the direction shown, what would be the work done by the electric field on the charge?


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Edward F. Redish
Department of Physics
University of Maryland
College Park, MD 20742
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Last revision 17. October, 2005.