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

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