# Motional emf

1. Feb 25, 2010

### LucasGB

Suppose I have a conducting bar moving over a constant magnetic field. A Lorentz force arises on the charges that constitute the bar, polarizing the bar, and generating what is called motional emf.

How can I explain this from the bar's point of view? From its own reference frame, the bar is not moving, and the magnetic field is uniform. So what causes the emf?

2. Feb 25, 2010

### kcdodd

If you have a pure magnetic field, B, in a 'stationary' frame, then in the 'moving' frame there is a magnetic and electric field, B' and E'. So, from the bar's point of view, there is a real electric field pushing the electrons.

3. Feb 25, 2010

### LucasGB

But B is constant in direction and magnitude, all over space, so from the bar's point of view, the flux of B through anything isn't changing. So where does this electric field come from?

4. Feb 25, 2010

### kcdodd

The electric and magnetic fields look different depending on how fast you are moving. What you may see as a magnetic field only, looks like a magnetic + electric field to the bar. This type of "paradox" lead to the lorentz transformations, and eventually to special relativity. This just happens to be an every day example.

5. Feb 25, 2010

### netheril96

Do NOT change frame of reference in electromagnetic problems before you study electrodynamics since no matter how slow the relative speed of of the two frames,you must use Lorentz transformation to change the field

6. Feb 25, 2010

### LucasGB

I understand relativity but I'm trying to see this from a classical point of view. I'm trying to find out if from the bar's point of view there's any change in magnetic flux and therefore, induced electric field, but it doesn't seem to be so. So you're saying that classical electrodynamics, without relativity, does not have a satisfactory answer for this?

7. Feb 25, 2010

### netheril96

There is NO so-called "classical electrodynamics without relativity"
As I said,no matter how slow the speed is,you MUST use relativity in a change of frame of reference.

8. Feb 25, 2010

### LucasGB

Alright, so I rephrase: are you saying that if one does not know relativity, he cannot give a satisfactory answer to my question?

9. Feb 25, 2010

### bjacoby

netheril96 says "yeah" but "he" is wrong. Relativity has nothing to do with it.

The Answer is that if you have a region of space where there exists electric and magnetic fields you can measure those with meters. You get some values. Now if you could mount your meters on a railroad flatcar (without disturbing the fields) and go hurtling through the same space, Lo, you find that the meters now read different values for both fields!

If E and H are the original fields measured by stationary meters and E* and H* are the new readings by the moving meters and V is the velocity of the moving meters relative to the original ones considered stationary. We find that

E* = E + V X B

H* = H - V x D

Thus we find moving meters see additional fields (called Lorentz fields) that stationary meters do not measure.

These relationships only hold for V<<c which is to say speeds much less than the velocity of light and thus are NOT relativistic relationships but exist at all velocities much less than light speed.

OK? As you can see from the bar's point of view there is an electric field in the region equal to V X B. It is these relationships that lead many physicists to believe that electric and magnetic fields are not different entities since they seem exchangeable with frames.

10. Feb 26, 2010

### netheril96

OK,I admit that I was wrong

11. Feb 26, 2010

### LucasGB

I see, I think I have a better understanding now. But can I relate this to the more basic concepts introduced in electrodynamics, i.e. can I understand what happens from the bar's point of view by invoking "change of flux induces fields" arguments? The reason I ask is because I googled "Lorentz fields" and didn't find anything about it. In fact, if you google it between quotes, this discussion of ours features the first page!

12. Feb 26, 2010

### netheril96

"change of flux induces fields" applies only in a specified frame of reference.
The electric field here is not induced

Think about a cube which is painted red on one surface,and blue on an adjacent surface.
In the first frame you see only the red(the magnetic field);when you rotate the cube,or move your self(change the frame of reference),you see both the red and the blue surface(you find an electric field).Obviously,the blue here is not 'induced' by the red.It is there,but you can't see it at first.

13. Feb 26, 2010

### Born2bwire

Technically, that is still relativity and always will be relativity. Classical electrodynamics automatically satisfies the special theory of relativity. So whenever you use Maxwell's equations between any kind of reference frames you are implicitly using relativity even if the velocities would be considered to be non-relativisitic. This can be seen glaringly for example in the case for the force between two current wires. In the lab frame, the force between the two wires results from the magnetic fields acting on the other wire. However, you can look at it from the frame of the electron carriers. In this frame, the force is due to the force from the transformed electric fields. This arises no matter how slowly we assume the electron carriers appear to move.

Real quick, have to run, but I believe in the OP's case though, we do not need to use Lorentz transformations. By moving the bar through the static fields, we are effectively moving the charges on the bar through the field. Thus, we now have charges with a non-zero velocity by which the magnetic field can act on them via the Lorentz force. Of course, the appropriate Lorentz transformations for when we are in the frame of the bar should give us the equivalent forces via the electric fields that arise from the transformation of the original magnetic field.

14. Feb 26, 2010

### kcdodd

Except you are saying now there are additional fields, seemingly without any source or cause. You can't derive such equations from the base principle of galilean transformation (v' = v - v_0), and so you can't really call them non-relativistic. All you have done is taken the first order approximation of the lorentz transformation. If I am wronge about that, please correct me.

Last edited: Feb 27, 2010
15. Feb 26, 2010

### LucasGB

Thank you all, I consider my question to be answered.

16. Feb 26, 2010