# B EM Phenomenon: Magnetism from a Cathode Ray?

Tags:
1. May 27, 2016

### Chris Frisella

I have recently studied about relativity being the reason for magnetism. The example given was about a magnetic field generated from current down a long wire. When two such wires with current in the same direction were parallel to each other there was an attractive force between them because from the reference frame of the electrons, the protons in the opposite wire were condensed, therefore a net attractive force.

Now my question: Would a cathode ray in a vacuum create a magnetic field like the wire does? I wonder this because in the cathode ray beam there are no corresponding protons like there are in the wire so there would be nothing to attract to...or what???

Thanks,
Chris

2. May 27, 2016

### Simon Bridge

Welcome to PF;
Yes.

It's a good question because the usual description showing how special relativity gives rise to a magnetic force in a wire is restricted to that kind of example (with positive and negative charge present) only. Probably because the more general case is kinda hard to follow. In a nutshell, relativity gives moving charges a magnetic field because of the finite time for changes in the electric field to propagate.

http://farside.ph.utexas.edu/teaching/em/lectures/node125.html

3. May 27, 2016

### sophiecentaur

The density of charges in the cathode Rays is much less but the speed is much greater. Relative to the cathode Rays, there is still a relativistic difference in + and - charge density in any conductor (electromagnet / nearby wire). As for how it would interact with a permanent magnet field, the 'simple' SR explanation for two wires would still need to be modified to give Flemming's rule.

4. May 27, 2016

### ZapperZ

Staff Emeritus

In particle accelerators, we can make a non-destructive measurement of the charge of the particle beam, especially when they are in bunches. We can use what is called an Integrating Charge Transformer (ICT), which is nothing more than a toroid around the beam pipe (see pg. 19 and 20 of this presentation, which is from a particle accelerator school). The charges passing through is the current going through the coil, inducing a magnetic field and generating an induced current in a secondary winding.

So heck yes, moving electrons can generate magnetic fields, without needing any positive background.

Zz.

5. May 27, 2016

### Merlin3189

I'm only looking at this thread by accident, but I recently saw another thread discussing the drift velocity of electrons in a wire. So I was a bit puzzled by the explanation of the magnetic attraction as a relativity effect. The velocity quoted for electrons in a wire was of the order 10-5 m/sec. This is not the sort of speed I associate with relativistic effects ( more like 108 m/sec)

I don't doubt the explanation for a moment. I think I have even heard of it before. I just wondered if anyone had any simple comment to reconcile these ideas in my mind?
The only thing I can think of so far, is that the relativistic effect is indeed miniscule, of the order of (10-5)2/ (108)2, but that when you take account of the number of electrons in the wire, I suppose around 1020 per metre, it starts to enter the realm of normality again.

6. May 27, 2016

In the case of two charges moving parallel to each other, (or the currents in two wires), if you go to the rest frame of the electrical charges there is no magnetic field or magnetic force. (All you observe is electrostatic repulsion.) This would seem to indicate that the magnetic fields and forces are a relativistic effect even for the slower velocities.

7. May 27, 2016

### sophiecentaur

"So heck yes, moving electrons can generate magnetic fields, without needing any positive background. "
The 'pinch effect' In plasma beams would (?) need the + and - charges to be travelling at different speeds for a 'simple' SR explanation, I think.

8. May 27, 2016

### Chris Frisella

Thank you Simon and all; that was helpful! I would be interesting in seeing an experiment of this. I have searched all of youtube and haven't found any attempt to have multiple electron beams interact with each other in different ways (only with electromagnets). Perhaps I'll have to build an apparatus....

9. May 29, 2016

### Simon Bridge

You are thinking of an electron beam experiment equivalent to the one where two wires deflect or attract each other?
The trouble here is that two charged beams will repel each other just from the electric charge being the same ... drowning out the magnetic effect.
ie you'd need quite sensitive measurements to see the difference.

Wires don't have that problem since they are just about electrically neutral.

You are, in fact, demonstrating the magnetic properties of the beam when you deflect it in a magnetic field ... just like you deflect a wire carrying a current.
It's the same effect.

10. May 29, 2016

### sophiecentaur

A wire has + and - charges and the SR explanation works fine even for just one passing free electron. But where is there an SR model for two beams of electrons? (Is my point)

11. May 29, 2016

### Chris Frisella

I think I know what would happen if the beams were parallel. Now I am just wondering why an incoming beam perpendicular to the wire would receive a force which is parallel to the wire. I made a little graphic to illustrate what I think would happen. My question is why does that force exist?

Last edited: May 29, 2016
12. May 29, 2016

### sophiecentaur

That's yet another instance where an SR explanation seems to be lacking. Some well informed PF member should be able to put us out of our misery. Hellooooo out there?????

13. May 29, 2016

Staff Emeritus
Maybe you want to rethink what you wrote. First, the PF membership is not some cadre of trained seals at your beck and call. Second, this is a holiday weekend. And finally, what you ask for is simply unreasonable.

SR has no problem in calculating the force on a charge from an arbitrary collections of charges and currents. It can even do so starting from electrostatics, superposition and Lorentz transformations. What it cannot do is do this at a "B" level.

14. May 29, 2016

### Chris Frisella

Vanadium, do you have a basic cause>effect explanation to my question? Not interested in math proofs, just a logical explanation.

15. May 29, 2016

Staff Emeritus
A moving charge creates a magnetic field.

16. May 29, 2016

### Staff: Mentor

In general, the electromagnetic force that a point charge A exerts on a point charge B depends on the positions of A and B, and on their velocities (magnitude and direction). For historical reasons, we call the position dependent part of the force "electric" and the velocity-dependent part "magnetic."

17. May 29, 2016

To the OP: (Referring to the diagram=post # 11) The magnetic force that an electron in the beam will experience is given by $F=e(v \times B )$ where the $v \times B$ is a vector cross product. Once you compute the magnetic field $B$ from the current in the wire, you should be able to compute the force if you can estimate the electron velocity. From the vector cross product you can compute the direction of the force, with or without an estimate on the magnitude of the electron's velocity.

18. May 29, 2016

### Chris Frisella

Vandium, granted. Referring to my illustration, why would there be a force on the beam parallel to the current carrying wire? How does this force arise along that vector? The common SR explanation doesn't really connect to my example well because I don't see there being any charge directly perpendicular to the electron beam, you know what I'm saying?

19. May 29, 2016

The magnetic field $B$ from the wire is in a circular direction around it. (Comes from Ampere's law and/or Biot-Savart's law). (The $B$ is perpendicular to the moving current in the wire so that a $v \times B$ can be parallel to the current.( $v$ is electron beam velocity.))