How Do Moving Charges Behave Differently in Different Reference Frames?

[lovetruth]

I'm going to try to start from http://physics.usask.ca/~xiaoc/phys463/notes/note19.pdf" 's formula, and see if it matches the Lorentz transformed version.

Xiao's formula contains the retarded position r_p(t_r):
R=r-r_p(t_r), where t_r=t-R/c.

For a charge moving at constant velocity, the current position r_p(t):
r_p(t)=r_p(t_r)+v.(t-t_r)

I also define the displacement vector from the current position:
R'=r-r_p(t)

Writing in terms of R':
R'=R-Rβ
R'=((R-Rβ).(R-Rβ))^1/2=R/γ (R'.β=0 for a perpendicular location)
n-β=R'/γR'
1-n.β=(1-γR'.β/R')/γ²=1/γ² (R'.β=0 for a perpendicular location)

Xiao's Eq 10.65 has n-β/((1-n.β)³.R².γ²), which for a perpendicular location works out to γR'/R'³.

Thank you for the derivation of E field using Xiao's eqn. which perfectly agrees with the fitzpatrick eqn. 1538.
I am wondering whether the lienard-Weichert potential has been proven experimentally like coulomb law.

 

[lovetruth]

Also, are xiao eqn and jeffimenko equation are same?

 

[Dale]

I am wondering whether the lienard-Weichert potential has been proven experimentally like coulomb law.

The Lienard-Weichert potential follows directly from Maxwell's equations, so yes. In fact, it is much more general than Coulomb's law, which is only an approximation for a stationary charge. The LW reduces to Coulomb's law in that situation.

 

[atyy]

Thank you for the derivation of E field using Xiao's eqn. which perfectly agrees with the fitzpatrick eqn. 1538.
I am wondering whether the lienard-Weichert potential has been proven experimentally like coulomb law.

Also, are xiao eqn and jeffimenko equation are same?

I don't know about the Xiao and Jeffimenko equations, and I don't have detailed knowledge of an experimental proof of the Lienard-Wiechert potentials, but I would suggest looking at applications of the (generalized) http://en.wikipedia.org/wiki/Larmor_formula" .

More generally, the Lorentz transformations are a http://www.physics.ox.ac.uk/users/iontrap/ams/teaching/rel_B.pdf" of Maxwell's equations.

Einstein's contribution was not to propose the Lorentz transformations, but to modify Newton's second law to be consistent with the Lorentz symmetry of Maxwell's equations. Einstein was applying the same sort of reasoning you used when you said:

If the EM force is reduced by changing frame then, all 4 fundamental forces(EM,gravity,strong,and weak forces) should have 'magnetic counterparts force' which can reduce the net force by 1/gamma [like Gravito-magnetic(made-up term)]. These 'magnetic counterparts' must exist otherwise reality will not be same in every frame.

I don't know if gravity has a "magnetic" component (I don't think http://en.wikipedia.org/wiki/Gravitomagnetism" , Eq 22).

 

[pervect]

It's probably a bit off topic, but the Bel decomposition of the Riemann does break it down into four parts. It's common to call one the electric part, (or the electrogravitic tensor), another the magnetic part,and the third the topological part. I'm not sure about the fourth part - perhaps it's zero.

See https://www.physicsforums.com/showpost.php?p=1347429&postcount=10, the electric part of the Riemann, sometimes called the tidal tensor, is just R_{abcd} u^b u^d, where u is a timelike vector of some observer.

Chris mentions taking the "right hodge dual" to get the magnetic part, I'm not quite sure how that's done..

 

[atyy]

It's probably a bit off topic, but the Bel decomposition of the Riemann does break it down into four parts. It's common to call one the electric part, (or the electrogravitic tensor), another the magnetic part,and the third the topological part. I'm not sure about the fourth part - perhaps it's zero.

See https://www.physicsforums.com/showpost.php?p=1347429&postcount=10, the electric part of the Riemann, sometimes called the tidal tensor, is just R_{abcd} u^b u^d, where u is a timelike vector of some observer.

Chris mentions taking the "right hodge dual" to get the magnetic part, I'm not quite sure how that's done..

That sounds really interesting! The only introductory material on that I've found so far is Senovilla's http://arxiv.org/abs/gr-qc/0010095.

 

[qsa]

http://www.cosmolearning.com/video-lectures/lecture-38-lorentz-transformations-in-em-fields-9760/

 

[atyy]

http://www.cosmolearning.com/video-lectures/lecture-38-lorentz-transformations-in-em-fields-9760/

Looks like a great set of lectures - thanks for the link!

 

[qsa]

Looks like a great set of lectures - thanks for the link!

You are wellcome. I am not sure if you have already discovered his QM courses, but here is the link anyway,



http://www.cosmolearning.com/courses/quantum-physics/

also the profs wikipedia page



http://en.wikipedia.org/wiki/V._Balakrishnan_(physicist )

 

[lovetruth]

I don't know about the Xiao and Jeffimenko equations, and I don't have detailed knowledge of an experimental proof of the Lienard-Wiechert potentials, but I would suggest looking at applications of the (generalized) http://en.wikipedia.org/wiki/Larmor_formula" .

More generally, the Lorentz transformations are a http://www.physics.ox.ac.uk/users/iontrap/ams/teaching/rel_B.pdf" of Maxwell's equations.

Einstein's contribution was not to propose the Lorentz transformations, but to modify Newton's second law to be consistent with the Lorentz symmetry of Maxwell's equations. Einstein was applying the same sort of reasoning you used when you said:



I don't know if gravity has a "magnetic" component (I don't think http://en.wikipedia.org/wiki/Gravitomagnetism" , Eq 22).

Thanks for the insight.