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State Faraday's Law of electromagnetic induction, both qualitatively and quantitatively. How is Lenz's Law included in this?

Faraday’s Law of electromagnetic induction states that the emf induced in a conductor is directly proportional to the rate of change of magnetic flux. Quantitatively, it is written in the following equation:

Note the use of the time derivative - this shows that we are observing how magnetic flux changes with each instantaneous interval of time.

Lenz’s Law separately addresses the direction of this induced emf - i.e. the induced emf ultimately induces a current who’s magnetic field opposes the change that induced it. Fortunately, we don’t need a separate equation for this, because it is already included in the above equation using the negative sign!

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