Question
Explain why a constant magnetic field does no work on a point charge moving through the field. Since the field does no work, what can we say about the speed of a point charge acted on only by a magnetic field?
Step 1
Step 1: Understand the Lorentz Force The force exerted on a point charge \( q \) moving with velocity \( \mathbf{v} \) in a magnetic field \( \mathbf{B} \) is given by the Lorentz force equation: \[ \mathbf{F} = q (\mathbf{v} \times \mathbf{B}) \] This force is Show more…
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The magnetic force cannot do work on a charged particle since the force is always perpendicular to the velocity. How then can magnets pick up nails? Consider two parallel current-carrying wires. The magnetic fields cause attractive forces between the wires, so it appears that the magnetic field due to one wire is doing work on the other wire. How is this explained? a) The magnetic force can do no work on isolated charges; this says nothing about the work it can do on charges confined in a conductor. b) Since only an electric field can do work on charges, it is actually the electric fields doing the work here. c) This apparent work is due to another type of force.
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