# Magnetic fields and relativity

1. Feb 21, 2010

### Jedimasta

i have several questions which relate to a project i will be starting soon
we all know the right hand rule and others, but does it apply to 2 particles interacting with each other? for example if 2 protons are moving towards each other

-------+>
<+---------

like that ^

will relativity affect them, causing the magnetic fields to make them repel each other more strongly than they would if they were stationary next to each other?

if they were 0.000,000,001m away from each other, and travelling at half the speed of light relative to each other, how much of the force pushing them apart would be from the magnetism at their closest point? (travelling perpendicular to each other)

also i need the relevant equations to answering this question so that next time i have a similar question, i can solve it myself

EDIT: does magnetic field strength generated by a single particle increase in strength linearly or exponentially? (if a proton doubles its velocity, does its magnetic field strength double? or quadruple?)

Last edited: Feb 21, 2010
2. Feb 21, 2010

### bcrowell

Staff Emeritus
This may helpful: http://www.lightandmatter.com/html_books/7cp/ch06/ch06.html [Broken] (section 6.2). See especially figure m.

Last edited by a moderator: May 4, 2017
3. Feb 21, 2010

### Naty1

yes relativity will affect attraction/repulsion: Columbs law strictly holds only for static (stationary) point charges. I have never seen the adaptation to a relativistic formula...I would not even venture a guess, but I betcha it's interesting....

4. Feb 21, 2010

### Jedimasta

i noticed in that article it says that if a proton and an electron were moving in the same direction, they would experience magnetic repulsion

if this were true, it would mean magnetism is NOT relativistic, since if it was, then those particles would experience no magnetic fields from each other, since relative to each other, they are stationary (while technically this effect would be observed if the same effect was tried with power cables *i will explain it if i have to, but its complicated, and a real pain in the *** to do*)

i need a 100% sure answer to my questions

also if someone could post the relevant equations to my second question it would be much appreciated

Last edited by a moderator: May 4, 2017
5. Feb 22, 2010

### clem

The relativistic expression for dp'/dt of a particle due to another particle is given by:
$$\frac{d{\bf p'}}{dt}=\frac{qq'[{\bf r}+{\bf v'\times(v\times r)}]} {\gamma_v^2[{\bf r}^2-({\bf v\times r)^2}]^{\frac{3}{2}}}.$$

But, this is only true for the first particle moving with constant velocity v.
If that particle accelerates, which is likely, then the equation becomes more complicated and requires use of the retarded time, making it almost intractable.

6. Feb 22, 2010

### Bob S

For two parallel or anti-parallel charged-particle beams, there are both Coulomb and magnetic forces. The forces are essentially the same for individual particles and for particle beams, but understanding the beam-beam interaction is a little easier than the particle-particle forces because of the transient effects with individual particles. The Coulomb force and the magnetic force are opposite for parallel beams, and cancel for very relativistic beams. See attachment. For anti-parallel charged-particle beams, the Coulomb and magnetic forces are additive.The same equations in the attachment can be used, but the sign of the force in equation [3] et. seq. should be changed. For currents in wires, there is no Coulomb force between the wires.

Bob S

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7. Feb 22, 2010

### Jedimasta

ok thanks for the help guys, much appreciated