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Classical education of EMF generation usually starts with something like this: Wire in a magnetic field

Where a wire is placed within a magnetic field and moved to create EMF. Or this: Magnet moved within a coil

Where a magnet is moved within a coil.

In both of these examples, the conductor has magnetic flux lines cutting and traveling through it.

In a generator, the stator is usually constructed with teeth holding the coils. These teeth focus and channel the flux, so that the flux path is through the teeth: the flux is concentrated within the teeth.

Generator Example

In this way, how is EMF generated if no flux actually cuts through / crosses the conductors, but rather travels between them?

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  • \$\begingroup\$ To stay in that simplistic picture, the flux crosses the conductors. See how during the clockwise movement of the rotor, the flux first in going along the rotor direction, then against it, then along again? \$\endgroup\$ – Janka Jul 6 '17 at 9:50
  • \$\begingroup\$ The flux is concentrated in the teeth. If you plot |B| across the slot, it is ~0 across the windings, then high across the tooth, then ~0 across the other side of the coil. There is no flux in the windings \$\endgroup\$ – wevcore Jul 6 '17 at 10:06
  • \$\begingroup\$ Please step back to the two-pole machine first. Then you see how the flux is going right through the rotor, and back through the shell. \$\endgroup\$ – Janka Jul 6 '17 at 10:12
  • \$\begingroup\$ @wevcore the diagram of the alternator would not work as shown and the flux would be, as you imply constant in each stator pole hence unchanging. The diagram is flawed I believe and neither does it clearly hint at any output terminals or what causes the north and south poles. \$\endgroup\$ – Andy aka Jul 6 '17 at 10:12
  • \$\begingroup\$ @Andy Aka: No, that diagram is ok. It's just that the OP ignores the flux arrows through the rotor for some unknown reason. \$\endgroup\$ – Janka Jul 6 '17 at 10:15
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You have a misunderstanding here. Moving the wire in the flux is not the trick. The trick is to change the flux that goes through a wire loop. Moving a part of that wire loop so that the moving part cuts the flux lines is only one way to change the flux throug the loop. Other ways, such as rotating a magnet (a permanent one or electric) inside a generator also cause changing flux through a wire loop (=through the winding).

If we watch carefully your generator, we can see moving wires that cut the flux. Here is still no need for deeper explanations than you had in your 2 first images. But there are generator types which have no moving wires cutting the flux.

Another useful thing to know:

The emf in a generator or as well in the secondary winding of a transformer is not an interaction between the wire and the magnetic field. The emf exists as circular electric field around the changing flux. That's the induction. Metal wires conduct the electric field field for us to use. That conducting is known as influence. Having several turns in a winding is the way to have the emf connected several times in series.

This all probably sounds complex and distracting. In physics one can easily spot the following equation: F = qV x B, (=Magnetic Lorentz force) where F is the vector force on a moving charge q and B is the surrounding magnetic flux density vector. That equation easily explains the generators where a wire moves cutting the magnetig flux. But that equation is only another formulation for the much deeper fact. Actually the induction and other by magnetism caused forces are complex three party interactions where the parties are the charges that move and the space. My knowledge of relativistic electrophysics is practically worthless so it's no use to write any more some gorgeous sentences that I have heard. Except one: Electric and magnetic fields are simplified formulations of those interactions, simple but still accurate enough for everyday electrical engineering works and so rich in content that the special theory of relativity could be found from the basic equations of electric and magnetic fields.

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how is EMF generated if no flux actually cuts through / crosses the conductors, but rather travels between them?

Think about an AC transformer: -

enter image description here

Theoretically, there is no flux crossing the conductors i.e. magnetic lines of flux are passing through the inside of each turn of wire.

The point is that any piece of wire can have a voltage induced in it by a changing magnetic field providing the lines of flux ARE NOT perfectly aligned in the same direction as the wire.

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  • \$\begingroup\$ This is more akin to what I was asking and is another example: No flux directly cuts the conductors but rather travels between them. I think I'm just taking the generic examples of classic EMF education too literally, and the EMF doesn't have to directly cut the conductors but can travel between them..? \$\endgroup\$ – wevcore Jul 7 '17 at 8:04
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    \$\begingroup\$ @wevcore The flux can be on the inside or the outside or a bit of both or even come in at most angles (except sideways) and, providing that the flux is changing and has some net value when integrated across the plane of the coil (to infinity), there will be an induced voltage. \$\endgroup\$ – Andy aka Jul 7 '17 at 11:19
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There are an infinite number of lines of flux crossing the air gap between the stator teeth and the rotor. There are many conductors on the rotor. As the rotor turns, the conductors move through the lines of flux.

The circles in the air gap between the rotor and the stator represent the cross section of the rotor windings. Current in the windings is flowing towards (.) and and away (x) from the viewer.

enter image description here

This AC generator has the armature on the rotor. In order to bring the generator current out, there must be slip rings and brushes. The output terminals are connected to the brushes. AC generators usually have the field on the rotor and use the armature as the stator.

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