# How is it that the induced EMF in an alternator is in quadrature with the main flux?

Looking at the simplified diagram of an alternator, the flux "linked" with the conductor is maximum at 90, 270 degrees, is also when induced EMF is maximum. So isn't the main flux in phase with the induced EMF, or are my assumptions flawed?

It's important to note that in an alternator, motional EMF is created which depends on the spatial angular displacement between an uniform magnetic field and a conductor perpendicularly placed. A time varying EMF is induced only because the angular displacement is a function of time, not the magnitude of the magnetic field itself.

At school I was taught that the voltage induced was proportional to the rate at which magnetic field lines were being cut by the windings. In reality the field lines don’t literally exist, but it’s a useful tool at an intuitive level. The EMF is in proportion to the rate of change in magnetic field that the coil experiences. Does that help?

• I'm not talking about the cutting of field lines. Its the angle between the magnetic field vector and the motion of the conductor that changes. From what I learned from the physics stackexchange, this is not an emf produced due to d(phi)/dt, but from the lorentz force effect. Seem obvious, the flux is constant only the angular displacement changes. If you're talking about the flux in inside the loop, then ignore the second conductor. Then there is not loop to have a d(phi)/dt Jan 16, 2021 at 8:41
• Have I misunderstood the question then?
– Frog
Jan 16, 2021 at 8:47
• On deep thought, there is another way to look a this,the flux through the loop is zero at when emf is maximum, such a way, emf and main flux are 90 degrees apart in time. So my assumption was flawed. I thought the link linkage was thought of as the flux linking with conductors individually, but in reality its assumed to be the flux linking with the coil itself. Only that way it makes sense on analyzing the armature reaction effects. Jan 16, 2021 at 8:56
• Thank you so much, if you didn't point out to think intuitively I couldn't have arrived at this conclusion. This question kept me awake all night. Being a EE graduate didn't help. Jan 16, 2021 at 8:57
• Ah yes, if the coil all moved in the same direction rather than rotating then there would be no EMF. I’m glad to hear you’ve cleared it up in your own mind.
– Frog
Jan 16, 2021 at 9:20

It's quite simple when you think about the spinning coil: -

Induced voltage is proportional to rate of change of flux so when the coil is at 90 ° (and spinning) it sees the biggest change in flux. At 0 °, when the coil is spinning the rate of change of flux is zero.