lecture19 - Magnetic Fields (II) Text sections 29.2 –...

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Unformatted text preview: Magnetic Fields (II) Text sections 29.2 – 29.3 •Force on a current-carrying wire (general case) •Torque on a current loop For practice: Chapter 29, problems 17, 19, 21, 23, 63 Review: Magnetic Forces Charged Particle : Straight wire, Uniform B: B v q F r r r × = B L I F r r r × = B not uniform, and/or wire not straight: the force dF on a short segment of vector length ds is I I Segment of length ds The total force on the wire is ∫ × = wire along I B ds F dF B ds dF = I ds x B Example 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 Total magnetic force = 0 Proof: { } B s d I B s Id F r r r r r × ∫ = ∫ × = BUT: for a closed loop! = ∫ s d r Theorem: For a closed current loop, in a uniform magnetic field, (if B is a constant vector) Torque on a Current Loop (Uniform B) w h θ B r a b d c Forces: x F ab = I w B sin θ F cd = I w B sin θ F bc = I h B F ad = I h B Example: a rectangular loop Top view:...
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This note was uploaded on 12/03/2009 for the course CHEMISTRY 1E03 taught by Professor Britz during the Spring '09 term at McMaster University.

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lecture19 - Magnetic Fields (II) Text sections 29.2 –...

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