# Static Magnetic Field and Work

by I done know
Tags: field, magnetic, static, work
 P: 5 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.
 Sci Advisor HW Helper P: 1,322 The force on a charged particle in a magnetic field is $$\vec{F} = q \vec{v} \times \vec{B}$$, 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?
 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.
HW Helper
P: 1,322

## Static Magnetic Field and Work

Wait, how did you conclude that $$\frac{d\vec{v}}{dt} = 0$$? The acceleration certainly isn't zero, there is a force acting.
 P: 5 Is it that the force is perpendicular to the magnetic field and work must be parallel to the displacement?
 Sci Advisor HW Helper P: 1,322 You are so close! The force is perpendicular to the field, but that's not what matters. What else is the force perpendicular to?
 P: 5 Ah, so because the force is perpendicular to the velocity, the force is perpendicular to the displacement.
 Sci Advisor HW Helper P: 1,322 Indeed. In simple terms, the power $$\vec{F} \cdot \vec{v}$$ is identically zero. Hence no work is done.

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