(1 (+-) v/c) factor in the Lienard Wiechert potentials

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In summary, the conversation discusses the justification for the (1-v/c) factor in Lienard and Wiechert's potential formula for a moving charge. The derivation can be found in many textbooks, including The Quantum Theory of Radiation by Heitler. The discussion also mentions the conservation of charge and the difference in interpretation between Heitler and Lienard and Wiechert. Ultimately, the conversation is interested in understanding the original arguments used by Lienard and Wiechert and a simpler derivation for the (1-v/c) factor.
  • #1
jason12345
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Does anyone know how either Lienard or Wiechert justified the (1-v/c) factor that appears in their potential formula for a moving charge?
 
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  • #2
The derivation is in many textbooks.
 
  • #3
clem said:
The derivation is in many textbooks.

How do you know their interpretation is the same as that of Lienard and Wiechert?

In my copy of The Quantum Theory of Radiation by Heitler, for example, he uses the idea of a collapsing spherical wavefront with velocity c centred on the field point that samples the charge within a volume dv. He then says that within a time dt as the spherical wavefront moves a distance dr, charge is added or removed from the volume dv, compared to if it the charge inside was static and hence gives rise to the additional term rho v/c.

Yet this charge entering/leaving the volume element is compensated by charge leaving/entering another volume element so the net effect is that there is a change in the charge density which is compensated by the change in the volume occupied by the charge as the wavefront sweeps through it. This means the total charge sampled by the wavefront should be conserved, whereas the Lienard Wiechert expression shows that it isn't.

Hence, I'm interested in knowing what arguments Lienard and Wiechert originally used.
 
  • #4
I think you are referring to a factor [tex](1-{\hat r}\cdot{\vec v}[/tex] introduced into the expression for the power radiated into a solid angle, and not a factor in the L-W potentials. Heitler's description is a bit convoluted, but gets the right factor.
A simpler derivation (probably not L's or W's) is that that factor equals
[tex]\frac{dt}{dt_r}[/tex] where [tex]t_r[/tex] is the retarded time.
 

1. What is the (1 (+-) v/c) factor in the Lienard Wiechert potentials?

The (1 (+-) v/c) factor in the Lienard Wiechert potentials is a correction factor that takes into account the velocity of the source and the speed of light in the equations. It accounts for the fact that the electromagnetic fields created by a moving charged particle are different from those created by a stationary charged particle.

2. How does the (1 (+-) v/c) factor affect the Lienard Wiechert potentials?

The (1 (+-) v/c) factor affects the Lienard Wiechert potentials by changing the shape and magnitude of the electromagnetic fields. It causes the fields to become distorted and shifted in the direction of motion of the source.

3. Why is the (1 (+-) v/c) factor important in the Lienard Wiechert potentials?

The (1 (+-) v/c) factor is important in the Lienard Wiechert potentials because it allows us to accurately calculate the electromagnetic fields generated by a moving charged particle. Without this correction factor, our calculations would not be as precise and would not match experimental results.

4. How does the (1 (+-) v/c) factor relate to special relativity?

The (1 (+-) v/c) factor is a consequence of special relativity, which states that the laws of physics must be the same for all observers moving at constant velocities. This correction factor accounts for the differences in the electromagnetic fields observed by different observers moving at different speeds.

5. Is the (1 (+-) v/c) factor always necessary in the Lienard Wiechert potentials?

No, the (1 (+-) v/c) factor is only necessary in cases where the source of the electromagnetic fields is moving at a significant fraction of the speed of light. For stationary sources, the factor becomes equal to 1 and has no effect on the potentials.

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