EM Phenomenon: Magnetism from a Cathode Ray?

  • #1
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
 

Answers and Replies

  • #2
Simon Bridge
Science Advisor
Homework Helper
17,857
1,655
Welcome to PF;
Would a cathode ray in a vacuum create a magnetic field like the wire does?
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.
Try it just for a single charge to start with.

http://farside.ph.utexas.edu/teaching/em/lectures/node125.html
 
  • #3
sophiecentaur
Science Advisor
Gold Member
2020 Award
25,474
5,002
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
ZapperZ
Staff Emeritus
Science Advisor
Education Advisor
Insights Author
35,847
4,672
Another addition to this.

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
Merlin3189
Homework Helper
Gold Member
1,655
769
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
Charles Link
Homework Helper
Insights Author
Gold Member
2020 Award
4,860
2,187
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.
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
sophiecentaur
Science Advisor
Gold Member
2020 Award
25,474
5,002
"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.
 
  • Like
Likes Charles Link
  • #8
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
Simon Bridge
Science Advisor
Homework Helper
17,857
1,655
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
sophiecentaur
Science Advisor
Gold Member
2020 Award
25,474
5,002
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
You are thinking of an electron beam experiment equivalent to the one where two wires deflect or attract each other?
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?

MagnetQuestion.jpg
 
Last edited:
  • #12
sophiecentaur
Science Advisor
Gold Member
2020 Award
25,474
5,002
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?????
 
  • Like
Likes Chris Frisella
  • #13
Vanadium 50
Staff Emeritus
Science Advisor
Education Advisor
26,350
9,835
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?????
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
Vanadium, do you have a basic cause>effect explanation to my question? Not interested in math proofs, just a logical explanation.
 
  • #15
Vanadium 50
Staff Emeritus
Science Advisor
Education Advisor
26,350
9,835
A moving charge creates a magnetic field.
 
  • Like
Likes Simon Bridge
  • #16
jtbell
Mentor
15,727
3,882
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."
 
  • Like
Likes Simon Bridge and Delta2
  • #17
Charles Link
Homework Helper
Insights Author
Gold Member
2020 Award
4,860
2,187
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
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
Charles Link
Homework Helper
Insights Author
Gold Member
2020 Award
4,860
2,187
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?
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.))
 
  • #20
Understood, JT, thank you. Charles, thank you, perhaps I need to clear up "vector cross product".
 
  • #21
Charles Link
Homework Helper
Insights Author
Gold Member
2020 Award
4,860
2,187
Understood, JT, thank you. Charles, thank you, perhaps I need to clear up "vector cross product".
In a vector cross product, the result is always perpendicular to the two vectors of the product. Another item is, if the two vectors are parallel, the vector cross product is zero.
 
  • #23
sophiecentaur
Science Advisor
Gold Member
2020 Award
25,474
5,002
Vanadium, do you have a basic cause>effect explanation to my question? Not interested in math proofs, just a logical explanation.
A moving charge creates a magnetic field.
That isn't an 'SR explanation'. The Magnetic Field explanation (Flemming's Rules) is well known and it's the standard one we start with. I think what we're after is something along the same lines as the SR explanation for the force between two current carrying wires. That doesn't need an explicit Magnetic Field and it is unlikely that there is not a suitable Non-Magnetic Field answer for moving electron situations.
P.S. I was not 'demanding' and answer in my previous post; I was simply saying that there "must" be such an explanation. "Trained Seals" we are not.
 
  • Like
Likes Chris Frisella
  • #24
Delta2
Homework Helper
Insights Author
Gold Member
3,559
1,374
I 've to say I don't know much about relativity but are we dealing here with cases where classical physics provide us with a simpler explanation but relativity give us a much more complex explanation (yet might explain it just a bit better).

For example using classical physics the moving electrons of the beam constitute a current density , hence they create a magnetic field due to Ampere's Law and this magnetic field just exerts a force on other nearby moving charges regardless if they are electrons or protons..
 

Related Threads on EM Phenomenon: Magnetism from a Cathode Ray?

Replies
5
Views
750
Replies
12
Views
4K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
7
Views
3K
  • Last Post
Replies
0
Views
4K
  • Last Post
Replies
12
Views
3K
  • Last Post
Replies
8
Views
3K
  • Last Post
Replies
11
Views
2K
  • Last Post
Replies
4
Views
853
Top