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# lecture18 - Magnetic Forces and Torques Review Charged...

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Magnetic Forces and Torques

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Review: Charged Particle in an external field : Straight wire of length L with current I in a uniform external field B: B v q F × = F I L B = Note: L points in direction of positive current flow
If B not uniform, and/or wirenot straight: theforce dF on a short segment of vector length dL is I I Segment of length dL The total forceon thewire is: along wire F IdL B = u uu u dF B dL dF = I dL x B Force on a current-carrying wire (general case)

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Example 1 y x x x x x x x x x x I (uniform) R θ Find theforceon: a) Thestraight wire b) Thesemicircular wire c) Thewhole circuit For (b): start with force dF due to an infinitesimal piece, and do theintegral. B
Solution

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Total magnetic force on the loop = 0 Proof: { } F IdL B I dL B = = uu uu But: for a closed loop, so F = 0 0 dL = uu Theorem : For any closed current loop in a uniform magnetic field, (if B is a constant vector)
Torque: Although thereis no net force on a circuit in a uniform field, theremay bea net torque. The torques due to

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lecture18 - Magnetic Forces and Torques Review Charged...

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