Induced current in a moving bar on rails

[khaled hayek]

Homework Statement

2 movable conducting bars on a conducting rail with a uniform magnetic field heading inside the paper , what will happen to bar 2 if we move bar 1 to the left with a velocity v ?

3. The Attempt at a Solution
i think that a current will be induced in bar 2 and pass to bar 1 via the rail , as a result , the magnetic field will affect bar 1 with a magnetic force and move it to the left (force on a current carrying wire) , but will there be a repel force between the two bars because a current passes through both of them (force between two parallel current-carrying wires) , and will that force stop bar 1 from moving left ?

 

[cnh1995]

https://www.physicsforums.com/posts/5464675/
Here is a thread from past. See of it helps..

 

[rude man]

, " ... and will that force stop bar 1 from moving left ?"

You have just stated that the #1 bar is being moved to the left with velocity v so how can it then be stopped from moving?

 

[haruspex]

You have just stated that the #1 bar is being moved to the left with velocity v so how can it then be stopped from moving?

It depends how you read the problem statement. Did we merely set the bar moving left at some speed v, or are we continuing to force it left at that speed?
The thread linked in post#2 relates to the former. I agree that as worded here it sounds more like the latter.

 

[rude man]

This seems lika good problem if properly defined. One could assume that at t=0 the left bar is d away from the right bar, moving with velocity v₀, the right bar is initially stationary w/r/t the external B flux lines. Interesting - bars 1 and 2 push each other apart by μ₀i²/2πd while the current with the B field imparts a force on each bar il x B. Meanwhile the current i = B⋅(l x v')/R, R = loop resistance which varies with t also, while v' has to take both bars' velocities into account. Quite a smörgåsbord, the quantitative solution of which was possibly not contemplated in the problem statement.