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Study Guide Concept Question on Magnetic Fields

  • #1

Homework Statement


Why are magnetic forces not always conservative?

I came across this question and to my knowledge they are always conservative....can anyone explain why they wouldn't be?
 

Answers and Replies

  • #2
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one way do define a force is one for which the associated force field has zero curl, in other words if

[tex]\nabla \times B = 0[/tex]

then the magnetic force is conservative. but, if there are currents, then

[tex]\nabla \times B = \mu_o J[/tex]

and so the curl is non-zero and the force is not conservative.
 

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