Well, this isn't much of a summary but remember this.
The flux changes according to the current, so same shape.
But you know, the field strength = -potentiala gradient of the flux.
Or E = d(flux)/dt (faraday's law)
so if the shape of the flux against time is like a sine curve. d/dt (sin t) = cos t.
So the E will be like a cos t starting from (0,1)
And as you know the phase difference b/w sine and cos curve is 90 degrees.