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Static Magnetic Field and Work

  1. Mar 30, 2006 #1
    Why can't a static magnetic field (not changing in time) ever do work? How do I express this formulaically? My only guess is that work is zero for a closed path.
     
  2. jcsd
  3. Mar 30, 2006 #2

    Physics Monkey

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    The force on a charged particle in a magnetic field is [tex] \vec{F} = q \vec{v} \times \vec{B} [/tex], right? Stare at that formula for a bit. Now ask yourself, how is the force related to the velocity? Then ask, how is work related to force?
     
  4. Mar 30, 2006 #3
    I see, then dv/dt is 0 when the B field is static, so if a=0 then F=0 then W=0. Sound right?

    Unfortunately this was on our last exam, and my answer was that W=qV and induced voltage is only a result of B flux changing in time.
     
  5. Mar 30, 2006 #4

    Physics Monkey

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    Wait, how did you conclude that [tex] \frac{d\vec{v}}{dt} = 0 [/tex]? The acceleration certainly isn't zero, there is a force acting.
     
  6. Mar 30, 2006 #5
    Is it that the force is perpendicular to the magnetic field and work must be parallel to the displacement?
     
  7. Mar 30, 2006 #6

    Physics Monkey

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    You are so close! The force is perpendicular to the field, but that's not what matters. What else is the force perpendicular to?
     
  8. Mar 30, 2006 #7
    Ah, so because the force is perpendicular to the velocity, the force is perpendicular to the displacement.
     
  9. Mar 30, 2006 #8

    Physics Monkey

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    Indeed. In simple terms, the power [tex] \vec{F} \cdot \vec{v} [/tex] is identically zero. Hence no work is done.
     
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