A wire of arbitrary shape connects points A and B and carries current I in a uniform magnetic field B. Which quantity determines the net magnetic force together with I and B?
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Question

A wire of arbitrary shape connects points A and B and carries current I in a uniform magnetic field B. Which quantity determines the net magnetic force together with I and B?

G1 Physics · Accepted Answer

F=I∫dℓ×B=I(rB−rA)×B for uniform B. Thus only the endpoint displacement matters.