Electrodynamics in two space dimensions :-(

In summary, the conversation includes a request for help with a problem and a solution that has been attempted but is not successful. There is also a suggestion to redo the solution in more detail and a private message exchange regarding potential familiarity between the speakers.
  • #1
ted1986
22
0
Hi all,

I've got this problem (which is attached as q1.jpg).

I've tried to solve it, but I'm stuck... my solution is also attached (my_sol1.jpg).

PLS help me :-(

Thnx

TED
 

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  • #2
In your derivation of the EOM, you got some indices wrong and forgot an A^μ. Maybe there are also sign or coefficient errors, haven't checked it in detail. I propose you to redo it in more detail.
For the next step, derive your EOM once and calculate ( θ η^{μν} - ε^{μνα} ∂_α ) J_ν using your EOM and the derived version, which should give you the left side.
 
  • #3
Thanks! I'll try it...

Do I know you from somewhere ? ;-)
 
  • #4
Don't know if I have seen you, but if you were born in 1986, that's possible ... you have a private message.
 
  • #5


Hello TED,

I understand your frustration with this problem. Electrodynamics in two space dimensions can be challenging to wrap your head around, but don't worry, I'm here to help.

Firstly, your solution looks correct so far. However, I noticed that you forgot to include the factor of 1/2 in your final equations for E and B. This is an important factor to include in two-dimensional problems.

Additionally, I would suggest checking your calculations for the electric and magnetic fields at the origin (x=0, y=0). This point is not included in your solution and it is important to check for consistency.

If you are still stuck, I would recommend breaking down the problem into smaller steps and carefully considering the equations for two-dimensional electrodynamics. Also, don't hesitate to reach out for further assistance.

Good luck!
 

FAQ: Electrodynamics in two space dimensions :-(

What is electrodynamics in two space dimensions?

Electrodynamics in two space dimensions is a branch of physics that deals with the behavior and interactions of electric and magnetic fields in a two-dimensional space. It is a simplified version of classical electrodynamics, which studies these fields in three-dimensional space.

What are the fundamental equations of electrodynamics in two space dimensions?

The fundamental equations of electrodynamics in two space dimensions are the two-dimensional versions of Maxwell's equations. These include Gauss's law for electric fields, Gauss's law for magnetic fields, Faraday's law of induction, and Ampere's law with Maxwell's correction.

What are some applications of electrodynamics in two space dimensions?

Electrodynamics in two space dimensions has various applications in fields such as condensed matter physics, quantum field theory, and cosmology. It helps in understanding the behavior of electrons in two-dimensional materials, the properties of particle interactions in two-dimensional systems, and the behavior of electromagnetic fields in the early universe.

What is the significance of studying electrodynamics in two space dimensions?

Studying electrodynamics in two space dimensions helps in understanding the behavior of physical systems in a simplified and more manageable way. It also provides insights into the behavior of fields and particles in lower-dimensional spaces, which can have unique properties and behaviors compared to higher-dimensional spaces.

What are some challenges in studying electrodynamics in two space dimensions?

One of the main challenges in studying electrodynamics in two space dimensions is the lack of experimental verification, as it is difficult to create and observe two-dimensional systems in a laboratory. Theoretical calculations and simulations are often used to study such systems, but they may not fully capture the complexities of real-world systems.

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