# Why is the electromotive force (EMF) highest in the loop when $\theta$ = $90$?

My question is in regard of the following snippet provided by my textbook.

So why is the electromotive force (EMF) highest in the loop when $$\theta$$ = $$90$$ or $$270$$?

So the magnitude of the induced EMF will be determined by the rate at which the loop is rotating, according to Faraday's Law. EMF will be maximum when the rate of change of flux is at maximum.

But why does this means that the loop has moved to a position parallel to the magnetic field and the flux through the loop is zero? Since there is no magnetic field penetrates the area at that instant shouldn't there be no current? In turns, shouldn't there be no magnetic field?

"Since there is no magnetic field penetrates the area at that instant shouldn't there be no current?"

I'm afraid that this is a bit like saying about a ball thrown upwards that has reached its highest point: "Since there is no velocity there can be no acceleration". In other words, you do need to consider carefully that it is rate of change of flux that matters, irrespective of the actual value of the flux. This rate of change at any instant is the slope of the tangent to the top graph at that instant. So just consider how that slope changes with time!

[There is another (more fundamental) way of understanding why the emf is a maximum when the coil has this orientation. Two sides of the coil (AB and CD) are parallel to the field lines; the other two, BC and DA are at right angles to the field. Because the coil is rotating, BC and DA are moving in opposite directions, at right angles to the field. Their velocity component at right angles to the field is greater than for any other orientation of the coil. Therefore the Lorentz force urging the free electrons in these sides of the coil is a maximum, so the e.m.f. is a maximum.]

The field mentioned in this discussion is from an external source. The maximum flux does occur when the normal vector representing the loop is parallel to the field (The field is passing through the loop), as indicated in the diagram. The maximum “rate of change” of the flux occurs when the plane of the loop is parallel with the field (and the normal vector is at 90 degrees.

1. The level magnets are exherting their normal N - pole and S - pole magnetic fields.

2. As the loop wire moves into 90*, the electric current going through the loop is also generating a secondary electro-magnetic field.

3. The interaction and clash between the 2 magnetic fields is the highest as the loop wire electromagnetic field is NEAREST the block magnets at 90*.

4. The magnetic interaction WEAKENS as the DISTANCE becomes longer when the loop MOVES AWAY from the 90* POSITION.