Chapter 31: Faraday's Law

• Magnetic flux: Similarly to the flux of any other quantity, the flux of B through a surface S is

  Φ_B = ∫_S B · dA .

• Faraday's law: When the magnetic flux through a closed loop C changes in time,

= –N dΦ_B/dt ,   or    ∫_C E · ds = – dΦ_B/dt .

• Lenz's law: The direction of the current induced around a loop of wire by a change in magnetic flux is such that the magnetic field it produces opposes the change in flux; If there is no actual wire, the emf is in the direction that would produce such a current.

• Motional emf: The potential difference induced across a conductor of length l (perpendicular to the velocity and to B) moving with velocity v in a direction perpendicular to a magnetic field B is

= –Blv .