Magnetic Force on wires? even just explanation?

Question

I don't even think my prof gave us the formula...obviously i could do the math..anyone know it off the top of their heads??

A straight wire of length 0.68 m carrying current 1.18 A is placed transversely to a magnetic field of strength 1.63 T. Determine the strength of the magnetic force on the wire.

Answer 1

You know that the Lorentz force is q v B, right?

If the entire wire is filled with charges dq = Q dx / L, so that Q = ∫ dq, and if all of them are going at some constant speed v, then each dq stays in the wire for a time L/v, which means that the current is I = Q v / L.

But the force must be ∫ v B dq. But v and B are constant. So it's just Q v B = L I B.

(Think about it in dimensional analysis terms, if that doesn't work for you. You need to replace the "q v" in q v B, but qv has units of coulombs * meters / second, which is the same as the units of I L.)