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Static Magnetic Field and Work

by I done know
Tags: field, magnetic, static, work
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I done know
#1
Mar30-06, 06:28 PM
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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.
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Physics Monkey
#2
Mar30-06, 06:36 PM
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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?
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#3
Mar30-06, 07:07 PM
P: 5
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.

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#4
Mar30-06, 07:16 PM
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Static Magnetic Field and Work

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.
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#5
Mar30-06, 07:37 PM
P: 5
Is it that the force is perpendicular to the magnetic field and work must be parallel to the displacement?
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#6
Mar30-06, 07:47 PM
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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?
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#7
Mar30-06, 07:54 PM
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Ah, so because the force is perpendicular to the velocity, the force is perpendicular to the displacement.
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#8
Mar30-06, 07:59 PM
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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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