Faraday's Law of Induction states that a change in magnetic flux through a loop induces an electromotive force (EMF) in the wire. The induced EMF is directly proportional to the rate of change of magnetic flux.
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The formula for Faraday's Law is $\mathcal{E} = - \frac{d\Phi_B}{dt}$ where $\mathcal{E}$ is the induced EMF and $\Phi_B$ is the magnetic flux.
Lenz’s Law helps determine the direction of the induced current, stating that it will oppose the change in magnetic flux that produced it.
Magnetic flux ($\Phi_B$) is given by $\Phi_B = B \cdot A \cdot \cos(\theta)$, where $B$ is the magnetic field, $A$ is the area, and $\theta$ is the angle between them.
Faraday's Law applies to both closed loops and coils, with coils having an EMF multiplied by the number of turns ($N$): $\mathcal{E} = - N \frac{d\Phi_B}{dt}$.
Practical applications include generators, transformers, and inductors which all operate based on principles from Faraday’s Law.