How Can Kirchhoff's Law Help Solve a Magnetic Circuit Problem?

[jimmycnj99]

I need help understanding how to solve a problem given by my professor for homework.

Please see the attached image. In this problem, there is an electric circuit with B=0.15 Tesla. There are 2 conductors moving in either direction - the left is at v = 4 m/s, the right is v =8 m/s. The resistance is 10 Ohms and 15 Ohms respectively. The length of the conductors is 1.2m. The professor wants to know the current in the 5 Ohm resistor in the middle of the picture. He said that Kirchoff's Law would be essential in solving this problem.

Any help would be appreciated!

Thanks,
James

 

[Doc Al]

What have you done so far?

Hint: First figure out the motional EMF in each conductor.

 

[jimmycnj99]

I think I would use the following for motional emf -

emf = vBL

Left bar would be 4 m/s * 0.15 T * 1.2m = 0.72 V/m
Right bar would be 8 m/s * 0.15 T * 1.2m = 1.44 V/m

Not sure what the next step would be...

 

[Doc Al]

I think I would use the following for motional emf -

emf = vBL

Left bar would be 4 m/s * 0.15 T * 1.2m = 0.72 V/m
Right bar would be 8 m/s * 0.15 T * 1.2m = 1.44 V/m

Good! Except that the units should be V, not V/m.

What's the direction of each EMF?

So now that you know the motional EMF in each branch, draw a picture of the equivalent circuit. Then you can start applying Kirchhoff's laws.

 

[jimmycnj99]

The direction of EMF(right) should be couterclockwise as I think it's opposite of the sign (+1.44V). The direction of EMF(left) should then be clockwise (-0.72V).

But I really don't understand Kirchoff's law and need some more advice on how to solve...

 

[Doc Al]

The direction of EMF(right) should be couterclockwise as I think it's opposite of the sign (+1.44V). The direction of EMF(left) should then be clockwise (-0.72V).

OK. The specific direction of each EMF depends on the direction of the magnetic field. But the main thing is that they are in opposite directions.

But I really don't understand Kirchoff's law and need some more advice on how to solve...

Sounds like you'd better review Kirchhoff's laws before worrying about this problem. Review your textbook or have a look here: http://theory.uwinnipeg.ca/physics/curr/node8.html" . (Be sure to click to the following page where you'll find several problems worked out.)