Magnetic flux

To understand induction, we first need a quantity: the magnetic flux Φ. It measures the "amount of magnetic field" passing through a surface, for instance the inside of a coil. It depends on three things: the field strength B, the area A of the surface, and above all the orientation of the surface relative to the field.

   Φ = B · A · cos(θ)      (θ = angle between the field and the normal to the surface)

   surface facing the field   tilted surface          parallel surface
   (θ = 0, cos = 1)           (any θ)                 (θ = 90°, cos = 0)
     ->|                       ->/                      ->  __
     ->|  MAXIMUM flux         -> /  reduced flux       ->     ZERO flux
     ->|                       ->/                      ->  __

When the surface faces the field (θ = 0), the flux is maximal. When it is parallel to the field (θ = 90°), no line crosses it: the flux is zero. Flux is measured in webers (Wb), where 1 Wb = 1 T·m².

The essential idea for what follows: the flux changes if you modify any one of these three quantities — the field B, the area A, or the angle θ. Bringing a magnet closer (B increases), rotating a coil (θ changes), deforming a circuit (A changes): in each case, the flux through the circuit varies. And it is precisely this variation of flux that will, as we shall see, give birth to a current.