Lorentz Force and Coulomb Force

In summary, the problem involves two identical point charges moving at a distance r apart and with speed v in frame S. To determine the force each charge exerts on the other, two approaches are suggested: using the Lorentz force and the field of a moving charged particle, or transforming the Coulomb force from the particle's rest frame to frame S. The equations F = q(e + (U X B)/C) and F = ke(q1q2/r^2) are relevant for these approaches. While the transformation of E and B can be done using covariant and contravariant forms, the first approach remains unclear. The hint provided by the teacher suggests using topic 6 slide 15 from [PLAIN]www.physics
  • #1
SpaceTrekkie
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Homework Statement



In frame S, two identical point charges q move abreast along lines parallel to the x-axis, a distance r apart and with speed v. Determine the force in S that each exerts on the other:

a) using the lorentz force in conjunction with the field of a moving charged particle
b) by transforming the Coulomb force from the particle's rest frame to the frame S


Homework Equations


F = q(e + (U X B)/C)
F = ke(q1q2/r^2)

The Attempt at a Solution



For a) I am not sure how to incorporate r into the equation (i assume that u and v are the same for this problem...meaning I can use v in the equation instead of u. I think it has to do with the field of a moving charged particle, but I can't see how that relates in a way that I can use.

For b) I am not sure how that could be transformed. I know how to transform E and B using the covarient and Contravarient forms. And I don't see how the speed would fit into that...does it go back to the basic lorentz factor, that has v in it.
 
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  • #2
okay I think I figured out the second one. It is a lot simpler than I was thinking. But 1, I still have no idea. My teacher's hint was use www.physics.gmu.edu/~joe/PHYS428[/URL] topic 6 slide 15. But I do not see how that would work out...
 
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What is the Lorentz Force?

The Lorentz Force is the force experienced by a charged particle in an electric and magnetic field. It is given by the equation F = q(E + v x B), where q is the charge of the particle, E is the electric field, v is the velocity of the particle, and B is the magnetic field.

What is the Coulomb Force?

The Coulomb Force is the force of attraction or repulsion between two charged particles. It is given by the equation F = k(q1 * q2)/r^2, where k is the Coulomb constant, q1 and q2 are the charges of the two particles, and r is the distance between them.

What is the relationship between Lorentz Force and Coulomb Force?

The Lorentz Force is a combination of the electric and magnetic forces, whereas the Coulomb Force is solely an electric force. The Lorentz Force is used to calculate the motion of charged particles in both electric and magnetic fields, while the Coulomb Force is used to calculate the interaction between two stationary charged particles.

What is the difference between Lorentz Force and Coulomb Force?

The main difference between the two forces is that the Lorentz Force takes into account the velocity of the charged particle, whereas the Coulomb Force does not. The Lorentz Force also includes a magnetic component, while the Coulomb Force is solely an electric force.

How are Lorentz Force and Coulomb Force used in everyday life?

The Lorentz Force is used in a variety of applications, including particle accelerators, electric motors, and cathode ray tubes. The Coulomb Force is used in everyday objects such as magnets, batteries, and electronic devices. Both forces are essential in understanding and manipulating electricity and magnetism, which are crucial in modern technology.

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