Describe the induced electric potential difference resulting from a change in magnetic flux.

Faraday’s law describes the relationship between changing magnetic flux and the resulting induced emf in a system. \[\mathcal{E} = - \dfrac{d \phi_B}{dt}\]

When the area of the surface being considered is constant, the induced emf is equal to the area multiplied by the rate of change in the component of the magnetic field perpendicular to the surface.

When the magnetic field is constant, the induced emf is equal to the magnetic field multiplied by the rate of change in area perpendicular to the magnetic field.

When an emf is induced in a long solenoid, the total induced emf is equal to the induced emf in a single loop multiplied by the number of loops in the solenoid. \[| \mathcal{E}_{sol} | = N | \dfrac{d \phi_B}{dt} |\]

Lenz’s law is used to determine the direction of an induced emf resulting from a changing magnetic flux.

An induced emf generates a current that creates a magnetic field that opposes the change in magnetic flux.

The right-hand rule is used to determine the relationships between current, emf, and magnetic flux.

Maxwell’s equations are the collection of equations that fully describe electromagnetism. Maxwell’s third equation is Faraday’s law of induction, which describes the relationship between a changing magnetic flux and an induced electric field. \[\mathcal{E} = \oint E \cdot dl = - \dfrac{d \Phi_B}{dt}\]

Maxwell’s equations can be used to show that electric and magnetic fields obey wave equations and that electromagnetic waves travel at a constant speed in free space. \[c = \dfrac{1}{\sqrt{\mu_0 \epsilon_0}}\]