How to Determine the Force on a Wire Frame in a Magnetic Field?

[edge]

Here is the problem:

Consider a rectangular wire frame moving through a region of uniform magnetic field of strength B. The rectangular wire frame has dimensions L x 2L. You pull the wire frame with a constant force F and it does not accelerate. The resistance of the wire frame is R. (The known quantites are B, F, L, and R). Determine the following in terms of only the known quantites:

1. The force exerted on the coil as a result of the induced current.
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This is where I have my trouble. I would normally want to use F = BIL and I = BvL/R since I'm used to seeing a similar problem where there is a velocity given instead of a force. It's annoying because I'm sure it's something simple I'm overlooking relating to the force... any help would be greatly apprecaited :)

Some of the other questions for this problem that I haven't been able to attempt (since I can't figure out the first) that might have some trouble with are...

Time rate of change of the magnetic flux.
Time rate of change of the area in the magnetic field.
Speed at which you are pulling the wire frame.
Direction of the induced current around the wire frame.

Any possible hints at how to approach those four would be appreciated. Thank you for your time!

-edge

 

[Doc Al]

net force is zero

Consider a rectangular wire frame moving through a region of uniform magnetic field of strength B.

I presume the coil is moving into or out of that region of uniform magnetic field.

This is where I have my trouble. I would normally want to use F = BIL and I = BvL/R since I'm used to seeing a similar problem where there is a velocity given instead of a force. It's annoying because I'm sure it's something simple I'm overlooking relating to the force... any help would be greatly apprecaited :)

You are overlooking the obvious. The coil does not accelerate. The applied force is given as F. So, what must be the magnetic force?

 

[Gokul43201]

Also, you need to specify in the problem - other than the point Doc Al made - which way the rectangle is being pulled, ie: parallel to the length or the breadth ?

And sure, you can use F = BVL/R - assuming the pulling force is parallel to 2L. But what you get out of it is V, the induced EMF (V is NOT a velocity), since all other quantities are known. From there, you use Faraday's Law to find the other quantities.