The figure shows a wire of arbitrary shape carrying a current i between points a and b. The wire lies in a plane at right angles to a uniform magnetic field B. Prove that the force on the wire is teh same as that on a straight wire carrying a current i directly from a to b. (Hint: Replace the wire by a series of "steps" that are parllel and perpendicular to the straight line jkoining a and b.) WEll umm well the force on the stirahgt wire from a to b is simply [tex] F = iL \cross B = iLB \sin( \theta)[/tex] for the arbitrary wire [tex] F = \int idL \cross B [/tex] but i is constant and B is constant so [tex] F = iB \int dL = iBL [/tex] whicvh is the same as the stariaght wire. Is this correct?