A question about electromagnetic induction

[Jackson Lee]

Hey, guys, I encountered this and confused about it.
"In a perfect conductor, an arbitrarily large current can be induced, and the resulting magnetic field exactly cancels the applied field."
But I suppose, according to Faraday's law,the magnitude of emf is the rate of change of magnetic flux, then if its resistance is zero, its current will be very large, so net magnetic flux as well and definitely not zero.
What do you think about it?

 

[Jackson Lee]

Besides,I want to know, if there is a loop of the same geometry and very small resistance, is it possible that induced magnetic flux larger than original flux?

 

[shubham agn]

Let us say we are decreasing the magnetic flux through a perfect conducting loop by varying the magnetic field. Then there will be an induced emf and as you rightly said, its magnitude will be very large on account of the very small resistance of the loop. So this induced emf will manage to nullify the decrease in the magnetic flux but the problem is that it may overshoot (because of its large magnitude) and in fact increase the magnetic flux. But as soon as there will be an infinitesimal increase, again a reverse emf will be induced which will try to nullify this increase, but which may again overshoot (because this too is very large). This infinite regress of "large" positive and negative emfs creates a changing current which is just such as to nullify the change in the magnetic flux through the loop. To prove this rigorously may not be easy, but that's what will happen. Thus, the induced magnetic flux will never be allowed to exceed the original flux because as soon as it tries to exceed, a reverse flux is immediately setup to decrease it.

 

[Jackson Lee]

Let us say we are decreasing the magnetic flux through a perfect conducting loop by varying the magnetic field. Then there will be an induced emf and as you rightly said, its magnitude will be very large on account of the very small resistance of the loop. So this induced emf will manage to nullify the decrease in the magnetic flux but the problem is that it may overshoot (because of its large magnitude) and in fact increase the magnetic flux. But as soon as there will be an infinitesimal increase, again a reverse emf will be induced which will try to nullify this increase, but which may again overshoot (because this too is very large). This infinite regress of "large" positive and negative emfs creates a changing current which is just such as to nullify the change in the magnetic flux through the loop. To prove this rigorously may not be easy, but that's what will happen. Thus, the induced magnetic flux will never be allowed to exceed the original flux because as soon as it tries to exceed, a reverse flux is immediately setup to decrease it.

Dear shubham, so you mean, if the induced magnetic flux exceed the original flux, then there will be no flux because all of them will be eliminate immediately?

 

[shubham agn]

Dear shubham, so you mean, if the induced magnetic flux exceed the original flux, then there will be no flux because all of them will be eliminate immediately?

Dear Jackson, what I mean to say is the following: Let us say the original flux through the loop is 10 Wb. Now, nature abhors a change in flux, so it will try to maintain it at 10 Wb at all times. Now, we decrease the flux to 9 Wb in a small time. Because of this changing flux, there will be an induced emf which is going to be proportional to the rate of decrease. But this emf will generate a very large current due to the small resistance of the loop. Now your doubt is that this large current may create a very large flux which may exceed the original flux i.e. 10 Wb. The induced flux is very large, so it will succeed in compensating the decrease in flux, it will take the flux back to 10 Wb, but will overshoot as you are saying. But as soon as it exceeds 10 Wb a little bit, let's say it takes the flux to 10.01 Wb, again an emf will be induced to oppose this increse in flux (because the loop likes the flux to be 10 Wb) and the flux will not be allowed to become arbitrary high. Thus, the induced flux will not be allowed to become arbitrarily large as we may think. And as I said earlier, this infinite cycles of positive and negative fluxes goes on such that the flux is infact maintained at 10 Wb. Hence it is said that the magnetic flux through a perfect conducting loop is always constant.

 

[Jackson Lee]

Dear Jackson, what I mean to say is the following: Let us say the original flux through the loop is 10 Wb. Now, nature abhors a change in flux, so it will try to maintain it at 10 Wb at all times. Now, we decrease the flux to 9 Wb in a small time. Because of this changing flux, there will be an induced emf which is going to be proportional to the rate of decrease. But this emf will generate a very large current due to the small resistance of the loop. Now your doubt is that this large current may create a very large flux which may exceed the original flux i.e. 10 Wb. The induced flux is very large, so it will succeed in compensating the decrease in flux, it will take the flux back to 10 Wb, but will overshoot as you are saying. But as soon as it exceeds 10 Wb a little bit, let's say it takes the flux to 10.01 Wb, again an emf will be induced to oppose this increse in flux (because the loop likes the flux to be 10 Wb) and the flux will not be allowed to become arbitrary high. Thus, the induced flux will not be allowed to become arbitrarily large as we may think. And as I said earlier, this infinite cycles of positive and negative fluxes goes on such that the flux is infact maintained at 10 Wb. Hence it is said that the magnetic flux through a perfect conducting loop is always constant.

Oh, your explanation is fantastis, I got it!Thanks very much