Electric forces between conducting rod and rail

[jisbon]

Homework Statement

A rod of length L and mass m can slide on vertical rails and is height H above a wire when both carry the same current I in opposite directions. If current in the lower wire is suddenly doubled, what is the initial acceleration of rod?

Relevant Equations

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Alright, to start off:

I'm not even sure how this works in the first place. What I do understand is that if they carry current in the opposite direction, using right-hand grip rule, the magnetic field between them will be the same (into the page). Hence using the left-hand rule, I can deduce that there is a magnetic force produced from the wire and rail vertically upwards (in this correct?)
So to remain the at equilibrium at height H, both rod and wire must produce the same force (is this correct?)
However searching through my notes and stuff, I found out both wire and rods to have the same formula for magnetic force $#(F=BIL sin \theta)$

Not sure how to proceed on here, what's the 'theory' behind this question? Any guidance will be appreciated. Thank you!

 

[jisbon]

Realized this question was similar to the one I posted few weeks back. I'm supposed to find I in terms of m and L. Since the rod remains in equilibrium at height L, is it ok to assume then $\epsilon =(\mu_{0}I/2\pi L)(L)(0)$
I'm not sure how to find the current if its equlibirum