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Magnetic Forces

  1. The Lorentz force on a charged particle due to electric and magnetic fields is
    F = q (E + v ⊗ B)
    The magnetic field B is measured in Tesla (1 T ≡ 1 N / (A m)). If E is 0, F is always perpendicular to v and acts as a     centripetal acceleration.

    If E = 0 and the charges are part of a current element I moving in the direction dl,

    F = I ∫ dl ⊗ B

  2. For a current loop with n loops and area A, define the magnetic moment:
    μ = n I A
    The direction of μ is most conveniently given by the right hand rule: if the fingers of your right hand follow in the direction of the current, your right thumb points in the direction of the moment.

    Then in a magnetic field, τ = μ ⊗ B and U = - μ ⋅ B.

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©2010, Kenneth R. Koehler. All Rights Reserved. This document may be freely reproduced provided that this copyright notice is included.

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