# Can a magnetic fields/forces do work on a current carrying wire?

Dale
Mentor
2021 Award
W = F.d (Work equals force times displacement due to the force along the direction of force).
That is the definition of work that is appropriate for Newtonian mechanics. It is not generally applicable when you are using fields as fields don't move (d=0) and fields can do work on other fields without any forces (F=0). The general definition that is applicable for fields is: work is a transfer of energy other than heat.

http://www.lightandmatter.com/html_books/lm/ch13/ch13.html#Section13.1 [Broken]

By Poynting's theorem the energy transfered from EM fields to matter (work) is E.j.

Last edited by a moderator:
That is the definition of work that is appropriate for Newtonian mechanics. It is not generally applicable when you are using fields as fields don't move (d=0) and fields can do work on other fields without any forces (F=0). The general definition that is applicable for fields is: work is a transfer of energy other than heat.

http://www.lightandmatter.com/html_books/lm/ch13/ch13.html#Section13.1 [Broken]

By Poynting's theorem the energy transfered from EM fields to matter (work) is E.j.

But energy is transferred to & from the B field as well. Using your definitions, the power source did the work, as well as the E forces, as well as the B forces. Since energy transfer involves all of these quantities, you can claim that either or all of them did the work.

Once again, it may be simply a matter of how "work done" is particularly defined. You stated earlier that fields & their forces do not move so that F.d is inadequate to describe work. But if I have a ball in my hand, then release it, dropping to the floor it acquires KE, what did the work? I only let go of it, applied no force. I say the gravity field did the work, although said field did not move. To me W = mgh is perfectly applicable here (h = height, m - mass. g = accel due gravity). The gravity field did work on the ball.

I can't understand how this question is even controversial. We know not all about e/m fields, but we know enough to answer the OP question. The force on the loop results in a torque which spins the loop, doing work, W = Iω2/2. This force is Fm = qvXB. E.J does indeed transfer energy, but the E component of Lorentz force, Fe, acts in a direction to move charges around said loop, not to spin loop.

My sketches illustrate this. Please, not just Dale, but all those in disagreement with moi, point out where my sketch is wrong. I'm not asking a lot by doing that.

Claude

Last edited by a moderator:
Dale
Mentor
2021 Award
But energy is transferred to & from the B field as well. Using your definitions, the power source did the work, as well as the E forces, as well as the B forces. Since energy transfer involves all of these quantities, you can claim that either or all of them did the work.
I am fine with this. This is, IMO, correct and is essentially the reason why I say that B can do work indirectly. The work done on matter is E.j but B has energy and influences both E and j.

But if I have a ball in my hand, then release it, dropping to the floor it acquires KE, what did the work? I only let go of it, applied no force. I say the gravity field did the work, although said field did not move. To me W = mgh is perfectly applicable here (h = height, m - mass. g = accel due gravity). The gravity field did work on the ball.
Yes, energy was transfered from the gravity field to the ball. The point is that B doesn't transfer energy directly to matter, only through E.j.

E.J does indeed transfer energy, but the E component of Lorentz force, Fe, acts in a direction to move charges around said loop, not to spin loop.

My sketches illustrate this. Please, not just Dale, but all those in disagreement with moi, point out where my sketch is wrong.
Your sketches aren't wrong, I have said that previously multiple times. They are just sketches of force, not energy transfer. As you yourself admit, the energy transfer is given by E.j.

That is the definition of work that is appropriate for Newtonian mechanics. [..]
The OP's questions are about mechanical work (moving wires, moving magnets). Throughout this thread I specified to which definition my answers related; sorry that I did not do so in every single post.
http://www.lightandmatter.com/html_books/lm/ch13/ch13.html#Section13.1 [Broken]
Yes, I think that I provided that link.
It also uses F.d. Where does it claim that this is wrong? (apart of energy loss which is not an issue here)

Last edited by a moderator:
Dale
Mentor
2021 Award
The OP's questions are about mechanical work (moving wires, moving magnets).
Yes, but mechanical work done by EM fields. So you need to use a general definition which can handle both the mechanical part and the fields part.

Yes, I think that I provided that link.
It also uses F.d. Where does it claim that this is wrong?
See section 13.6, and then in the summary he explicitly says "There are some situations in which the equation W=Fd is ambiguous or not true".

Yes, but mechanical work done by EM fields. So you need to use a general definition which can handle both the mechanical part and the fields part.
Concerning that aspect, I have no issue with W=F.d (and neither has either article).
See section 13.6, and then in the summary he explicitly says "There are some situations in which the equation W=Fd is ambiguous or not true".
Ah yes: d relates to the displacement of the point(s) where F is acting over that displacement (for lazy onlookers: a pushing hand does work but a rigid bouncing wall does zero work). And of course heat loss isn't work. None of that is an issue for answering the OP's questions.

Dale
Mentor
2021 Award
Concerning that aspect, I have no issue with W=F.d (and neither has either article).
I do (and you really are stretching credulity to claim that an article which says something is sometimes "ambiguous or not true" has "no issue" with it)

I do (and you really are stretching credulity to claim that an article which says something is sometimes "ambiguous or not true" has "no issue" with it)
Here you mis-cited me.