Faraday's law
Micheal Faraday was a exceptional visionary when it came to seeing the invisible. Even though his mathmatical skills where not up to those of Gauss he was able to visualize invisible physical effects in simple ways. Faraday's law is a result of his visualizations. Faraday saw that a changing magnetic field through a coil of wire produced a current in the wire. The direction of the current was such as to oppose the change of magnetic flux. This means that the current vectors and magnetic vectors are always 90 degrees out of phase. Notice in this animation that when the magnetic field vector is pointing up and decreasing the current flows counter clock wise. Does this agree whith Ampere's law if the current is trying to oppose the change of magnetic flux?