How can Lenz's Law be derived?

[acimarol]

Heinrich Lenz postulated in 1834 the following law;

"An induced current is always in such a direction as to oppose the motion or change causing it"

I have checked many undergrad/grad-level textbooks for a derivation, but they all just state Lenz's Law without derivation as if it were a universal law like the conservation of energy.

Can anyone help me with a derivation of Lenz's Law?

 

[Redd]

I don't know if you can really "derive" something like Lenz's Law.
Do you mean mathematically? because I don't know if that's necessarily possible,
its just an observed fact that if you (for instance) change the magnetic flux through a solenoid a current will be induced that will create a Magnetic field to oppose the change.
Perhaps intuitively you could think of it as a solenoid resisting changes to its B fields,
and following that logic it can be seen as a result of conservation arguments.

Its sort of like asking to "derive" the observed fact that a moving charged particle
feels a force perpendicular to the velocity of the particle and the B field;
its just what happens.

 

[jtbell]

Lenz's Law is the conseqence of the minus sign in the third of Maxwell's equations, which are the fundamental starting point for classical electrodynamics:

http://hyperphysics.phy-astr.gsu.edu/Hbase/electric/maxeq.html

 

[acimarol]

I don't know if you can really "derive" something like Lenz's Law.
Do you mean mathematically? because I don't know if that's necessarily possible,
its just an observed fact that if you (for instance) change the magnetic flux through a solenoid a current will be induced that will create a Magnetic field to oppose the change.

Yes, I am asking for some sort of mathematical proof. But what you say is reasonable, and I see where you are coming from.

Let's say a magnetic dipole is moving toward a coil with a constant velocity. I was mainly wondering if the part of Lenz's Law that says the induced magnetic field will oppose the motion of the magnet is a consequence of conservation of energy? Or am I interpreting Lenz's incorrectly, and it actually does not state anything about opposing the motion of the magnetic dipole?

 

[lubuntu]

Lenz's Law is the conseqence of the minus sign in the third of Maxwell's equations, which are the fundamental starting point for classical electrodynamics:

http://hyperphysics.phy-astr.gsu.edu/Hbase/electric/maxeq.html

I think you've got it a bit backwards, the minus sign I think is the consequence of the experimental fact. All it does is give the the direction of the E field, as you may remember are conventions for picking the directions of E and B fields are arbitrary. Frankly I think asking to derive Lenz's Law is like asking to derive the right hand rule, its just the result of an arbitrary choice of picking a direction. Reverse the directions and suddenly the "Law" says that the induced EMF supports the change in flux.

 

[Born2bwire]

I think you've got it a bit backwards, the minus sign I think is the consequence of the experimental fact. All it does is give the the direction of the E field, as you may remember are conventions for picking the directions of E and B fields are arbitrary. Frankly I think asking to derive Lenz's Law is like asking to derive the right hand rule, its just the result of an arbitrary choice of picking a direction. Reverse the directions and suddenly the "Law" says that the induced EMF supports the change in flux.

No, you cannot get the EMF to support the change in flux, that would violate energy conservation at the very least. If you changed the handed-ness convention consistently throughout the equations, you should preserve Lenz's Law.