Faraday's law and the electromagnetic wave, +B→-E or -B→+E

E and B are sine and cosine waves because they are ninety degrees out of phase. B is the cosine since it has a sign change in its derivative. Lenz's law comes from the sign change in the derivative. d(cos)/dt = -sin or d(-cos)/dt = sin. Faraday's law is applied twice per wavelength so there
is no net sign change per wavelength since, -1*-1 = 1. This sign change does not occur in Ampere's law, noting d(sin)/dt = cos or d(-sin)/dt = -cos, does not have a sign change.Our

When we divide the voltage on both sides of Faraday's law by the resistance of a loop or coil of wire then we get Ohm's law: volts/resistance = amps.

Integrals of Faraday's law

E*ds = -d(