Paradox of Magnetic Force: Exploring the Relationship between Magnetism and Work

[Abid Mir]

M

Good. And it's good that, according to BvU, Griffiths also attributes the work done to the power supply.

I don't quite agree with you here. It's not the magnetic field varying with time that induces the back-emf, or, equivalently that causes the 'backward' forces along the wire on the charge carriers. Rather, it's that the wire, and therefore its charge carriers, are moving through a magnetic field, and therefore experiencing a Magnetic Lorentz force, $q \mathbf{v} \times \mathbf{B}$. This can, if one wishes, be regarded as electromagnetic induction by means of flux cutting, but there's no need to use the terminology of e-m induction: the argument can all be carried through in terms of forces and work, as I did in post 12 and the handwritten continuation.

Note that all this is about forces due to the magnetic field. There is also an electric field, which exerts a force to the right on the charge carriers, opposing the magnetic force to the left, and which is set up by the power supply. This ultimately does the work. [Note that the force between electrons and ions is yet another force due to an electric field.]

magnetic force to the left?

 

[Philip Wood]

Yes, to the left, as in the hand-drawn diagram. This is the component of the magnetic force which arises from the upward motion of the wire. The other (upward) force component arises from the drift velocity of the charge-carriers along the wire.

 

[Abid Mir]

Yes, to the left, as in the hand-drawn diagram. This is the component of the magnetic force which arises from the upward motion of the wire. The other (upward) force component arises from the drift velocity of the charge-carriers along the wire.

Yeah k i got it ty

 

[Philip Wood]

Yeah k i got it ty

I assume that "ty" means "Thank you".
Does "k" mean "ok"?

It just occurred to me that my argument can be summed up like this:

A (cartesian) component of a magnetic force can do positive work, provided that the sum of the work done by all three components is zero.

The implies that if one component does positive work, at least one of the other two does negative work.

In the case we're considering, the component of force in the $\mathbf{k}$ direction is zero.

 

[vanhees71]

Hello Abid, Philip,

How come these threads rant on and on from one misunderstanding to the next misinterpretation, while it's so easy to read on a bit further and get it all handed on a silver platter ? And if at that point something is still unclear, it's easier to post very specific questions that allow much more compact answers !

That's one of the enigmas of human behavior too difficult for a simple minded physicist to explain. What can be simpler than the statement that
$$\vec{v} \cdot (\vec{v} \times \vec{B})=0,$$
which unambiguously proves that magnetic forces on a point charge do no work? Why people don't want to "believe" that, I can't answer; maybe a psychologist can ;-).