Electrodynamics in two space dimensions :-(

[ted1986]

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

 

[grey_earl]

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.

 

[ted1986]

Thanks! I'll try it...

Do I know you from somewhere ? ;-)

 

[grey_earl]

Don't know if I have seen you, but if you were born in 1986, that's possible ... you have a private message.

 

[paranormal]

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!