# Rigorous formulation of Lenz's law

I am wondering of how to apply Lenz's law to a jumping ring experiment as shown in the following picture: One migtht say that the direction of the induced current is such that the magnetic field in the ring, which is generate by the induced current is directed in a direction such that it opposes the change of $B_{\mathrm{Coil}}$.

If you choose the ring much smaller than the coil as in my picture above, you see that following one of the green field lines there are parts that oppose the rising $B_{\mathrm{Coil}}$ (inside of the ring) and also parts which are in the same direction of it.

So Lenz's law in this formulation doesn't give a clear indication of how the current would be.

How is the correct, rigorous formulation of Lenz's law and how to apply it in this case?

How to see in this example, why Lenz's law is nothing more then conservation of energy?

• The strongest magnetic field wins. Apr 23, 2018 at 12:45

You would be right to be concerned that there are many surfaces we can draw that are bounded by the ring; some of them would be like bubbles about to detach themselves from a child's bubble-blowing ring. But these surfaces will be cut by green lines going in an opposite direction to the blue lines! Try sketching it! [It's a very neat consequence of the Maxwell equation $\text{Div}\vec{B}=0\$ that the exact surface doesn't matter in cases like this, provided that it's bounded by the circuit in question.]