# L27_a - MAGNETIC FORCE ON A CURRENT-CARRYING CONDUCTOR...

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MAGNETIC FORCE ON A CURRENT-CARRYING CONDUCTOR (22.5) Important: basis of electric motors, microphones, speakers, transducers, etc. For wire carrying current I upward o d v q r is upwards for each charge o Force on EACH CHARGE points left (perpendicular to wire and field) B v q F d B r r r × = o Direction would be opposite for downward current Next want to write force in terms of current I B in F B

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MAGNETIC FORCE ON A CURRENT-CARRYING CONDUCTOR Force on each charge in wire is B v q F d B r r r × = How many charge carriers in a length l of wire? o For cross-section area A and n carriers per unit volume, number of carriers in length l is l A n SO: force on wire segment of length l is ( ) l A n B v q F d B r r r × = BUT: current in wire is A v q n I d = SO : force on length l of wire is B l I F B r r r × = o Vector l r points in direction of current; magnitude is length of segment I B in F B l A
Force on current-carrying wire of arbitrary shape: Divide wire into short, “straight” elements with

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## L27_a - MAGNETIC FORCE ON A CURRENT-CARRYING CONDUCTOR...

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