Circuit/magnetic field

[bsmack]

Homework Statement

A bar of length 22 cm that slides on two rails are connected together to make a complete electrical circuit. A magnetic field of strength 0.05 T directed out of the paper exists throughout the regions of space in which this machine is located. Assume that the distance between the rails l=20 cm and that initiaully the bar's sliding velocity is v=12 cm/s. Find the magnitude of the emf induced in this circuit.

Homework Equations

What equations should I be looking at? If it's an equation involving an integral, please give the final equation and possibly an explanation.

The Attempt at a Solution

The only equation I have available to me is emf = integ(E * dl). I don't know how I would get the electric field with the variables given, and I also don't know how I would get dl, as I don't think the length of the rails is given, just the length of the bar going across the rails and the distance between the rails.

 

[estel]

use the universal flux rule.

emf = d(phi)/dt = B da/dt = Bl dx/dt = B v

 

[bsmack]

So, my answer should be B*v=0.006 V? This is from a practice final, and the answer listed is 0.0012 V. Did we forget to multiply by 2 somewhere?

 

[Physics Monkey]

Check your units, bsmack. Does B v have the units of time derivative of flux? You see there is a slight typo in estel's final line. It should read $$B L v$$. What is the value of L for your system? (Make sure you pick the right one!)

 

[bsmack]

I think I figured it out. It should be emf = Bvl, correct?

 

[Physics Monkey]

Yes, you have it now. Just figure out what L is.