The Ring of Wire

There is a Johnny Cash song called the Ring of Fire. It has lyrics that include 'I went down, down, down, And the flames went higher.'

The magnetic field created by a current-carrying wire circles the wire. If your thumb points in the direction of the current, your fingers curl in the direction of the magnetic field (white arrows). The induced magnetic field is less than and opposes the external magnetic field (black arrows). Capital phi is flux, which equals the integral of B (the magnetic field) dA. With more B field pointing up, the flux through the area inside the ring does go higher. The force on a current carrying wire is F= integral of I dl cross B, where I is the current through the wire, l (L as in dl, sorry about this font) is the length of the wire, and B is the magnetic field. The emf is the integral (over a closed area) of the electric field dl (l=L is again the length of the wire) = -derivative of the flux with respect to time.