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Derivation of Lenz's Law

  1. Nov 19, 2009 #1
    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. jcsd
  3. Nov 19, 2009 #2
    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.
  4. Nov 19, 2009 #3


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    Staff: Mentor

  5. Nov 19, 2009 #4
    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?
  6. Nov 19, 2009 #5
    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.
  7. Nov 19, 2009 #6


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    Science Advisor
    Gold Member

    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.
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