Extended Coulomb's Law: Need Help w/ LaTeX

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The discussion revolves around the Extended Coulomb's Law formula, which is presented incorrectly and requires proper formatting in LaTeX. The correct LaTeX expression is provided, highlighting the need for clarity in the formula's components. Participants emphasize that the interaction of electric and magnetic fields is more complex than the initial formula suggests, and they recommend consulting advanced electromagnetic textbooks for accurate relativistic formulas. The original poster aims to establish an equilibrium forces equation, incorporating various forces, including fictitious ones, and seeks a formula related to electron velocity in atomic structures. Overall, the conversation underscores the importance of accurate representation and understanding of electromagnetic principles.
MARTIN LOPEZ
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I FOUND THIS EXPRESSION TO AN EXTENDED COULOMB´S LAW:

F = (k*q1*q2/r2)(1 -v2/c2)

BUT I NEED TO USE THE LATEX...HELP

SOMEBODY COULD HELP ME?
 
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MARTIN LOPEZ said:
I FOUND THIS EXPRESSION TO AN EXTENDED COULOMB´S LAW:

F = (k*q1*q2/r2)(1 -v2/c2)

BUT I NEED TO USE THE LATEX...HELP

SOMEBODY COULD HELP ME?

The formula is wrong, but in Latex it would be
F=q_1 q_2(1-v^2/c^2)/r^2.
 
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if you separate the formula, may be you can begin to understand it, just do it and we continue
 
MARTIN LOPEZ said:
if you separate the formula, may be you can begin to understand it, just do it and we continue
What does "separate" mean?
 
ok.

F = (kq1*q2/r2)*(1-v2/c2) = electric force (coulomb´s law) - magnetic force

F = (kq1*q2/r2) - (magnetic constant)*q1*q2*v2)/4*pi*r2

could some phenomena like this exists?
 
No, because the magnetic and electric fields of a moving particle are more complicated than you have assumed.
 
I´ve got two static charges in my hands and I measure the electric field, but I´m in a spaceship, just someone out of the spaceship see the magnetic field. How many complicated things see that observer?. I measure electric fields in the earth. What´s the traveling speed of the Earth around the Universe?
 
The relativistic formula for the fields of a moving charge are in most advanced EM textbooks. They enter to order v^2/c^2, which is too small to see with the Earth's velocity. But the v^2/c^2 correction to E is of the same order as the v^2/c^2 magneitc effect.
 
  • #10
What is the relativistic formula for the fields of a moving charge?
What is the relativistic formula for the forces of a moving charge?
 
  • #11
Grab an E&M book, as clem says, or look here: http://farside.ph.utexas.edu/teaching/jk1/lectures/node26.html"
 
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  • #12
I´ve got an article "Conceptual error in contemporary science", the author is: Joseph J. Smulsky. He presents a formula very similar to the formula shown in The electromagnetic field due to a uniformly moving charge. Which one is right?

I wanted to establish an equilibrium forces equation and I got the formula I present.

But F = (K*q1*q2/4*pi*r2)(1-v2/c2) it´s just a step for the complete equilibrium equation, there are more forces including fictitious forces.

I calculated using biot-savart law and lorentz force the magnetic force and I was adding terms to the equation.

Finally I wanted a formula for electron velocity in atomic structure
 

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