Study Guide Concept Question on Magnetic Fields

[lookingforhlp]

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?

 

[eczeno]

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

$$\nabla \times B = 0$$

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

$$\nabla \times B = \mu_o J$$

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