# 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 wire not straight: the force dF on a short segment of vector length dL is I I Segment of length dL The total force on the wire 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 the force on: a) The straight wire b) The semicircular wire c) The whole circuit For (b): start with force dF due to an infinitesimal piece, and do the integral. 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 there is no net force on a circuit in a uniform field, there may

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

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