# Magnetic Field and Work

This is a true or false question relating magnetic field and work:
A current-carryign wire placed in a magnetic field will gain kentic energy as the wire accelerates in response to the magnetic force. However, in applying the definition of work, ( W = F * D * cos x ), we realize that the magnetic field cannot do work on a charged particle because the force on the particle is perpendicular to its motion. Froom this we conclude that the magnetic force is an exception to the rule.

Personally, i think the statement is false. but I really can't find a way to prove it.
Can someone throw in some insight into this?

well the wire will have an induced magnetic field in the opposite direction (because it is a moving charge) and this will "cancel" out part of the original field. I'm not really sure of the technical terms, but it something to do with decreasing the magnetic field and since it takes energy to create a magnetic field, this energy is used to accelerate the wire.

Andrew Mason
Homework Helper
leolaw said:
This is a true or false question relating magnetic field and work:
A current-carryign wire placed in a magnetic field will gain kentic energy as the wire accelerates in response to the magnetic force. However, in applying the definition of work, ( W = F * D * cos x ), we realize that the magnetic field cannot do work on a charged particle because the force on the particle is perpendicular to its motion. Froom this we conclude that the magnetic force is an exception to the rule.
Is this comparing the magnetic force on a current carrying conductor placed at right angles to a magnetic field with a charge moving at right angles to the magnetic field?

For the moving charge, the magnetic field applies a force which is perpendicular to the charge's motion. As the charge moves, its direction of motion changes. But then, consequently, so does the force. As a result, the force is always at right angles to the direction of motion. In the definition of work: $W = FDcos\theta$ no work is done since the angle $\theta$ is always 90 degrees.

So I think the answer to the question is: True.

But the problem is that a moving charge passing through a magnetic field perpendicular to its motion will emit electromagnetic radiation and, therefore, it will lose kinetic energy.

So where does the energy comes from if the magnetic field does not do any work at all on the electron?

AM

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If it isn't the magnetic field, which is doing the work on charging particle, what other thing is doing the work? I know that it must have something working on the particles becasue W = fd.
Does it have anything to do with the premability of free space? Andrew Mason
Homework Helper
leolaw said:
If it isn't the magnetic field, which is doing the work on charging particle, what other thing is doing the work? I know that it must have something working on the particles becasue W = fd.
Does it have anything to do with the premability of free space? What makes you think that work is being done on the particle?

AM

Well, i think if it has force exerted on it, and it moves in a distance (particles in the wire accelerate perpendicular to the field), so W = F*d
That why i am thinking that something has done work on it. But the problem is that the Force is perpendicular to the magnetic field, thus the work done to the particle is F * d * cos 90, which would give us zero Joules.
Uh...i dont think i make sense, but if an object has force exerted upon it, it should have work done to it as well right?

jtbell
Mentor
There are other forces involved here besides the magnetic force on the electrons. Consider the difference in behavior between a beam of electrons (without a wire) traveling perpendicularly to the magnetic field, and a current of electrons in a straight wire that is oriented perpendicularly to the field. The beam curves in a circular path, but the wire stays straight and accelerates perpendicularly to its length. What does the wire have that the beam doesn't have?

It has a path (which is the cable) that the particles have to follow through

Let's assume that:

-the current is going upwards,
-Lorenz's force is directed to the left;

What would happen if there was no wire (the charged particles were in free space)? They would turn to the left.

The wire doesn't let them turn left (you guys are right: there is a path). So the particles are exerted not only to the magnetic force, but also to the force F of the reaction of the wire (it is directed to the right).

Accoarding to the 3d Newton's law the particles apply force T (T=-F) for the wire.

So, the work that accelerates the cabel is done by the force T.

NO EXCEPTION AND NO CONTRADICTION WITH THE CONSERVATION OF ENERGY PRINCIPLE! 