Can Faraday's Law Explain the Induced Current in Two Concentric Loops of Wire?

[matpo39]

I'm going over my practice physics exam and came to this question Two concentric, circular loops of wire lie in the plane of the paper. The outer loop carries a current I. pick the right answer.

I was able to get the choose to two:

a) If I is clockwise and increasing the induced current of the inner loop will be clockwise.

b) If I is counterclockwise and decreasing, the induced currecnt in the inner loop will be counterclockwise.

i know that answer is b, but i don't see how choice a) is wrong.

 

[Cyrus]

Lenz Law states that the second loop will set up a magnetic field to resist the change in the first one. If the current is decreasing, then the second loop wants to try to increase the magnetic flux, and visa versa. a.) can't be right, because the flux is increasing as the current increases, the second loop should try to compensate by decreasing the flux, but that won't happen if the current moves in the same direction in both wires. b.) is correct, because if current is decreasing in one direction, the magnetic flux is also decreasing. The current in the secound loop must move in the same direction to cause an increase in flux to make up for the drop.

 

[Theelectricchild]

I apologize if I sound silly for thinking this--- but is it appropriate to think of Lenz Law as a "conservation of magnetic field" law? For example if a loop is moving in a path where the magnetic flux is decreasing (say into the page), then a current will be induced in a clockwise manner in order to "fire" more B field into the page... hence conserving the magnetic field that was lost.. is this not a true law mainly due to that the amount of current induced to create B into the page not the same (in Teslas) that was previously lost?

 

[Cyrus]

Im just taking a guess but; in general, a conservative law says that if you travel around any closed interval and return to where you started, you did no net work. I don't see how this applies to Lenz Law. It has nothing to do with a closed path, or any path for that matter. It just says if flux goes down, the conductor will make flux go up through induction.

Thought about it some more, no, it clearly can't be conservative. Think about it. What if I decrease the current in the outer loop to zero? We would both readily agree that the second loop will not compensate by having the original current I going through it so that the flux remains constant. It would mean that the second inner loop has now assumed a full current I inside it that was once in the outer loop and maintains it at no cost. Maybe if it were a superconductor this might work though?

 

[Theelectricchild]

That explanation makes sense--- I would like to know the effects of a superconductor...

However going back to the Net Work = 0 argument--- The ACTUAL law called Conservation of Charge--- does that necessarily apply to this fact as well? All we are basically saying is that none of the charge is "destroyed" correct?

 

[Cyrus]

I think it would work in a superconductor. As the outer loops current decreases to zero, the inner loop would increase to the original amount of current in the inner loop, at which point it stops and just maintains that amount of current.

Im sorry I am not understanding what you mean with your conservation of charge statement, can you explain it a second time to me. The charge isint going anywhere, both wires have a net charge of zero at all times.