Magnetic force on sliding conductor moving through field

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CyberneticTitan
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Hello,

Please consider this diagram:

Diagram of a conducting bar sliding right at velocity v across two parallel rails in a uniform field B into the page, with resistor R at the left end and length l between rails, dx = v dt marked.


From the diagram, we can see there are two forces.

One: The Lorentz Force (qvB). Using the RHR, we can see that there is a force pushing north (up) to cause the separation of charges in the sliding conductor to establish the current in the loop.

Two: The Magnetic Force on a Current Carrying Wire (ILB). Orienting our index towards the direction of the current (north in the conductor) and the middle finger into the page, we can see that there is a resulting force pushing in the west direction (to the left).

Now these assumptions are generated if we are in the reference frames of the rails.

If the current is flowing north, and the velocity is oriented towards the right, would we consider that the direction of the current to be north-east? As a result, wouldn't the magnetic force be oriented slightly north-west?

Thanks!
 
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