Consider two parallel current-carrying wires. The magnetic...

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.

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.

Key Concepts

Magnetic Force on Moving Charges

Magnetic forces act perpendicular to the velocity of moving charges as dictated by the Lorentz force law. This perpendicularity means that the magnetic force changes only the direction, not the speed, of the charges, so it cannot do work on individual, free charges by altering their kinetic energy.

Work and Energy in Electromagnetic Systems

Although a magnetic field does no work on free charges, energy can still be transferred within electromagnetic systems. In circuits, for example, work performed on current-carrying conductors is attributed to energy supplied by external sources (such as batteries) or associated electric fields, not directly by the magnetic field.

Constraints and Confinement in Conductors

When charges are confined within a conductor, their motion is constrained by the structure of the material, meaning that forces can cause macroscopic motion of the conductor even if the microscopic magnetic forces individually do no work. The energy that appears to be used to move the conductor ultimately comes from the external work done by the power source, not from the magnetic field alone.

Transcript

00:01 At the magnetic force formula.

00:03 F magnetic equals qv cross b.

00:07 And one of the things that's true is that, number one, this is a formula for force for an isolated charge q.

00:16 That's the first thing to realize.

00:18 The second thing to realize is that this formula shows that the magnetic force can do no work on a moving charge because the magnetic field is always perpendicular to both the velocity and the force.

00:45 And probably in a better way to say that is that the force is perpendicular to the velocity, which means that the displacement of the particle will always be at a 90 degree angle to force and work equals force dotted into displacement.

01:10 So what we're going to look at is some reasoning for how it is then that two wires carrying currents in the same direction can actually attract each other so that the wires move closer together if the magnetic force can do no work.

01:30 And realize that that attraction will be perpendicular to the magnetic field produced by one of the wires.

01:42 So one of the important things to realize is that the charges are not isolated inside of the wires.

01:50 So i'll kind of draw a little sketch of what's going on and come up with a mechanism for how the attraction occurs.

02:00 And we'll see that in this case, what's providing the energy for the displacement to take place is basically the potential difference that's driving the current or the electric field that's set up in the wire to allow the current to continue to flow in the same direction.

02:23 Because this perpendicular force should make charges circulate in little circles.

02:29 And so whatever is driving the current is preventing circular orbits from taking over, so to speak.

02:40 Anyway, let's find the magnetic field of the left wire.

02:45 So we'll call that the left wire.

02:47 And we'll draw a picture of what's going on with the charges inside the right wire...

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