Lenz’s law states: the induced emf or current in a circuit opposes the change in magnetic flux.
Remarks:
- It is a qualitative law that specifies the direction of induced current but not its module.
- It is an alternative (and more intuitive) way the direction of the emf compared to Faraday’s law.
- It was formulated by the Russian scientist Emil Lenz (1804–1865) who independently from Faraday and Henry discovered it.
- Lenz’s law may be seen as analogous to Newton’s third law in classical mechanics.
- Lenz’s law is a consequence of the conservation of energy.
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#Slidewire generator revised
Applying Faraday’s Law to the slidewire generator we derive the same expression that we derived using the Lorentz force.
The minus sign indicates that the emf is directed counterclockwise around the loop.
The induced emf produces a current around the loop of magnitude $I=\mathcal E/R=BLv/R$. As a result, the rod experiences a magnetic force $\vec F=I\vec L\times \vec B$ opposed to the velocity (as an expression of Lenz’s law). To keep a constant velocity, the applied force must compensate the magnetic force, hence
$$ F=I L B=\frac{B L v}{R} L B=\frac{B^{2} L^{2} v}{R} $$One can also check that the work done per unit time on the rod $P_{applied}=Fv$ compensates the power dissipated by the circuit $P_{dissipated}=I^2R$ (conservation of energy).
- The slidewire generator transforms mechanical energy into electric energy, conserving energy in the process.
The equations
$$ \mathcal{E} = \oint (\vec{v} \times \vec{B}) \cdot d\vec{l} $$ $$ \mathcal{E} = -\frac{d\Phi_B}{dt} $$ are actually expressions of Faraday’s law. The former is more convenient formulation for moving conductors, while the latter is necessary for stationary conductors in changing magnetic fields.
Inductors