Proving DC Current Loop Does Not Radiate w/ Lienard-Wiechert Potential

In summary, the conversation discusses a question from Jackson's classical electrodynamics about proving that a dc current loop does not radiate using Lienard-Wiechert potentials. The problem involves considering the limit of q->0, \Delta->0, and N->Infty to obtain the Biot Savart law. The conversation also mentions using the Lienard-Wiechert potentials and attempting to solve the problem with no success. Finally, the conversation asks for a solution or hint for the problem.
  • #1
Rafa_Tapia
1
0

Homework Statement


Hi guys,
on chapter 14 in Jackson's classical electrodynamics, problems 24 asks to prove that a dc current loop does not radiate, starting from Lienard-Wiechert potentials for the individual charges q. The distance between them is \Delta.
We should move to the continuous media by considering q->0, \Delta->0 and N->Infty. Then, the fields should go to the known Biot Savart law. The charge's speed is constant but there exists an acceleration.

Homework Equations



We should use just the Lienard-Wiechert potentials.

The Attempt at a Solution



I've being trying this problem for a long time with no success. I've moved from q/Delta to a linear charge density and try to see the properties of the potential along the total path. I suppose the contributions should cancel out, but I don't get it for an arbitrary closed path.

Has any of you have the solution or at least some hint, it would be of great help!
Thanks a lot!
 
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  • #2
Rafa_Tapia said:

Homework Statement


Hi guys,
on chapter 14 in Jackson's classical electrodynamics, problems 24 asks to prove that a dc current loop does not radiate, starting from Lienard-Wiechert potentials for the individual charges q. The distance between them is \Delta.
We should move to the continuous media by considering q->0, \Delta->0 and N->Infty. Then, the fields should go to the known Biot Savart law. The charge's speed is constant but there exists an acceleration.

Homework Equations



We should use just the Lienard-Wiechert potentials.

The Attempt at a Solution



I've being trying this problem for a long time with no success. I've moved from q/Delta to a linear charge density and try to see the properties of the potential along the total path. I suppose the contributions should cancel out, but I don't get it for an arbitrary closed path.

Has any of you have the solution or at least some hint, it would be of great help!
Thanks a lot!
What is the (classical) expression for the energy density in terms of electric and magnetic fields?
 

1. What is the Lienard-Wiechert potential?

The Lienard-Wiechert potential is a mathematical concept used in electrodynamics to describe the electric and magnetic fields created by a moving charged particle.

2. How does the Lienard-Wiechert potential relate to DC current loops?

The Lienard-Wiechert potential can be used to calculate the electric and magnetic fields created by a DC current loop. This potential takes into account the movement and acceleration of the charged particles within the loop.

3. Why is it important to prove that DC current loops do not radiate?

Proving that DC current loops do not radiate is important for understanding the behavior of electromagnetic fields and for accurately predicting the behavior of electrical systems. It also helps to validate the laws of electrodynamics and the mathematical models used to describe them.

4. How has the Lienard-Wiechert potential been used to study DC current loops?

The Lienard-Wiechert potential has been used in theoretical and experimental studies to analyze the electric and magnetic fields created by DC current loops. It has also been used to develop mathematical models for predicting the behavior of these fields.

5. What evidence supports the claim that DC current loops do not radiate?

Experimental studies have been conducted to measure the electric and magnetic fields of DC current loops and have found that they do not exhibit any radiation effects. Additionally, theoretical calculations using the Lienard-Wiechert potential have also shown that DC current loops do not radiate. This evidence supports the claim that DC current loops do not radiate.

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