Extended Coulomb's Law: Need Help w/ LaTeX

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SUMMARY

The forum discussion centers on the Extended Coulomb's Law formula, specifically the expression F = (k*q1*q2/r2)(1 - v^2/c^2). Users provided feedback that the formula is incorrect and suggested the proper LaTeX representation as F = q_1 q_2(1 - v^2/c^2)/r^2. The conversation also touches on the complexities of electric and magnetic fields of moving charges, emphasizing the need for a solid understanding of electromagnetic theory and relativistic effects. Additionally, references to Physics Forums guidelines and advanced electromagnetic textbooks were made to guide the user in refining their understanding.

PREREQUISITES
  • Understanding of LaTeX formatting for scientific equations
  • Familiarity with Coulomb's Law and its applications
  • Knowledge of electromagnetic theory, particularly the behavior of moving charges
  • Basic principles of special relativity, including the significance of v^2/c^2
NEXT STEPS
  • Learn LaTeX for scientific documentation and formula representation
  • Study the derivation and applications of Coulomb's Law in electromagnetism
  • Research the relativistic effects on electric and magnetic fields in advanced E&M textbooks
  • Explore the Biot-Savart Law and Lorentz force to understand magnetic interactions
USEFUL FOR

This discussion is beneficial for physics students, educators, and researchers interested in advanced electromagnetism, particularly those working with LaTeX for scientific writing and those seeking to deepen their understanding of the interactions between electric and magnetic fields in moving charges.

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.
 
Last edited by a moderator:
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"
 
Last edited by a moderator:
  • #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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