Flux. The flux through one turn is the component of the field along the area vector, times the area: Φ = BA cos θ, where θ is the angle between the area vector (the normal to the loop) and the field. It is a maximum when the loop faces the field, and zero when the loop is edge-on.

Faraday’s law. The EMF is the negative rate of change of the flux linkage: EMF = −N dΦ/dt. With θ = ωt:

Φ = BA cos(ωt), EMF = −N dΦ/dt = NBAω sin(ωt), ω = 2π/T, A = πr²

Look at the two graphs. The EMF is largest where the flux graph is steepest, which is where the flux is zero. The EMF is zero where the flux graph is flat, at its maximum and minimum. The dashed tangent on the flux graph shows the slope: the EMF is −N times that slope.

What changes the EMF. The peak EMF NBAω is bigger for a stronger field, a bigger loop, more turns, or faster rotation (a shorter period).

The loop is drawn in two views: from above (looking down the axis of rotation), so you can see the angle, and looking along the field, so you can see how the area facing the field shrinks to nothing when the loop is edge-on. The graphs show one rotation.