# Derivation of Lenz's Law

1. Nov 19, 2009

### 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?

2. Nov 19, 2009

### 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.

3. Nov 19, 2009

### Staff: Mentor

4. Nov 19, 2009

### acimarol

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?

5. Nov 19, 2009

### lubuntu

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.

6. Nov 19, 2009

### Born2bwire

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.