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Moving Electric Charge Creating a Magnetic Field 
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#1
Jan710, 12:19 PM

P: 11

Does a moving charge create a magnetic field?
At first the answer was obvious to me, since I = Q/t then if a charge is moved it is simillar to an electric current, and electric currents create magnetic fields. However in a conductor, an electric current consists of electrons moving past relatively stationary protons. So I know there is a physical difference between moving a charge and an electric current. I am just wondering what the differences are, my guess is that the faster a charged particle moves the electric field get weaker and the magnetic field gets stronger. But i haven't been able to find anything helpful for my understanding. If anyone knows of any explantions or concepts to help understand what happens it would be appreciated. 


#2
Jan710, 12:49 PM

P: 836




#3
Jan710, 01:08 PM

P: 4,663

See my post #25 in
http://www.physicsforums.com/showthr...c+force&page=2 and this attachment http://www.physicsforums.com/attachm...6&d=1259869448 showing that the Coulomb field gets weaker, and the magnetic field gets stronger, as the velocity approaches c, where the two opposing forces cancel. Bob S 


#4
Jan710, 01:52 PM

P: 189

Moving Electric Charge Creating a Magnetic Field
I enjoyed your calculation....very straightforward and well written. 


#5
Jan810, 01:37 AM

Sci Advisor
PF Gold
P: 1,777

You can look up the LiénardWiechert potentials in most textbooks, like Jackson. They will give you the electric and magnetic fields for a charge of arbitrary trajectory. But you will find that you do not get an increase in the magnetic field versus the electric field. Once you have a moving charge, the radiation is electromagnetic waves. The electric and magnetic fields maintain a constant relationship between them. So if the electric field decreases, the magnetic field decreases by the same amount. This can be seen explicitly with either the potential or the field equations.



#6
Jan810, 10:46 AM

P: 4,663

In charged particle beams, the charge density of the beam produces a radial electric field that produces a repulsive force on individual particles. See Eqn (4) in Karlheinz Schindl's paper
http://cas.web.cern.ch/CAS/Loutraki...ndl/paper1.pdf Simultaneously, the current of the moving beam produces a magnetic field that produces an attractive force on individual particles. See eqn (8). These two opposing forces are combined in Eqn (9) to (11), cancelling each other as β → 1. The cancellation is proportional to 1/γ^{2}. Space charge forces, both Coulomb and magnetic, are well known in charged particle beams, and cause emittance blowup in lowβ, highcurrent beams. The two forces cancel for very relativistic beams. Bob S 


#7
Jan810, 09:03 PM

P: 11

Ok, i think i have a better understanding of the concepts, though i dont really understand
all of those formulas. If i were to keep it simple and just consider two moving point charges with the same charge and velocity. would the forces be? Electric Force F_{e}=k(q1 x q2)/d^{2} Magnetic Force F_{m} = (k(q1 x q2)/d^{2})(v^{2}/c^{2}) Net Force F_{N} = (k(q1 x q2)/d^{2})(1v^{2}/c^{2}) 


#8
Jan810, 11:17 PM

Sci Advisor
PF Gold
P: 1,777




#9
Jan910, 02:24 AM

P: 11

the problem i face with BiotSavart law and briefly looking at Jefimenko's equations from wikipedia.
http://en.wikipedia.org/wiki/Biot%E2%80%93Savart_law is finding the current or current density of a small charge such as an electron, or a point charge based on its velocity. The way i see it if dealing with a point charge that has any velocity will have infinite current. I was thinking I = (Q x v)/d where d is the diameter, and V is the Velocity, but this didn't seem to make sense when i looked at other equations. 


#10
Jan910, 02:44 AM

Sci Advisor
PF Gold
P: 1,777

Oh yeah my bad. I just realized I wasn't seeing the velocity dependence in the equations from Jackson, he takes his cross product of the electric fields using the directional vector for the retarded position, which has a term of v/c tucked away in there when you convert the vector from the retarded position to the instantaneous position. So the magnetic fields, for a constant moving charge, are proportional to the electric fields by the velocity of the charge. It would get a bit messy in general for a charge of arbitrary trajectory since the cross product is taken using the retarded position (which for an accelerating charge would be not be directly dependent on the velocity since the retarded position would follow an arbitrary path in time).
For Biot Savart, it's fairly easy, you just treat the point charge as an infinitesimal current element. But actually I found what I wanted to reference in the first place, tucked away further down the page are the equations for a particle of constant velocity. There are added terms that arise if the particle is accelerating, which is why I usually reference the LienerdWiechert potentials (though I haven't found an expression for the fields from them for a point charge on wikipedia though you can find them in Griffiths, Jackson, etc.). Jefimenko's equations aren't terribly useful for this problem, it would be annoying to work it out from them, I just forgot that the field equations I wanted to reference were buried on the BiotSavart page. So just look further down and they have the field equations derived from Maxwell's equations directly (not from BiotSavart though). Also, since the current element that the charge represents in space is localized, you would also want to have a dirac delta in your current statement. This is how they lose the integral when they use the BiotSavart law to find the magnetic field from a charge for the nonrelativistic expresion on the Wiki page. 


#11
Jan910, 12:17 PM

P: 4,663

The easiest way to calculate the vector magnetic and electric field components of a relativistic constantvelocity point charge might be just writing down the individual vector components of the isotropic electric field at a distance x=r·sin(θ) from a charge at rest, and Lorentztransforming them to the electric and magnetic components in the moving frame (including Lorentzcontraction z' = z/γ) using the four equations at the bottom of:
http://pdg.lbl.gov/2009/reviews/rpp2...relations.pdf This would avoid the problem of the pointcharge singularity in the BiotSavart Law. Bob S 


#12
Jan1510, 09:16 PM

P: 1

Actually, I have already learned that electrical building like a Mig Welding when I was in high school. But now that I am in college, I already forgot about it so I study again about it and found out that when an electrical charge is moving or an electric current passes through a wire, a circular magnetic field is created.



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