Conservation of Energy for Parallel Wires

[Essence]

Homework Statement

So I'm trying to prove to myself that energy is conserved in the case of magnetism. Here is the set up that I'm using to get that understanding (attached image).

Just to be clear the arrows represent the current lines and I am calculating a gain in PE because if I release Circuit 2 (after closing Circuit 1) I believe it will move in the direction of Circuit 1 (PE turns into KE).

Question: When I close the switch to Circuit 1 I create potential energy for Circuit 2. Where does the energy come from (I presume it comes from the current but don’t see how)?

Homework Equations

I suppose I could list the force equation

F = q v x B
This is really a baseline conceptual question; I already know how to calculate the force (I believe) and everything.

The Attempt at a Solution

N/A (Conceptual Question)

 

[Rmehtany]

Dear Essence,

Try the following thought experiment (it might help you.) You have a copper tube, and you drop a copper disk through it. Does the disk fall normally? Is it obstructed?

Hope this helps

 

[Rmehtany]

Try the following video: www.youtube.com/watch?v=keMpUaoA3Tg

 

[Essence]

So this video is a demonstration of induced current due to change in magnetic flux I believe. Are you saying that the law that this relates to will get me to the derivation of where the new potential energy by closing Circuit 1 comes from? Totally possible; just want to check. I believe my teacher mentioned how that law relates to energy conservation when I asked him if there was a more fundamental thought process that combines Maxwell's equations.

I will probably think about it more (because it bothers me that I only understand Maxwell's equations from the standpoint of a technician).

Thanks.