Magnet dimensions for 3-phase permanent generator I'm making a 3-phase permenant generator. According to Faraday's law, the emf produced is negative number of turns times the change in magnetic flux over the change in time. If it is only the CHANGE IN magnetic flux that is taken into account, why would it make a difference if I was using a 2x1x1/2 magnet or a 2x1/2x1/2?
 A: Note: For practical alternator designs for gaining experience you are MUCH better off looking at websites with construction examples that seem to meet your needs than trying to push the limits of what can be achieved and (typically) failing. You can leap straight into finite element analysis and more, but actually building something 

If it is only the CHANGE IN magnetic flux that is taken into account, why would it make a difference if I was using a 2x1x1/2 magnet or a 2x1/2x1/2?

There are several effects that cause practical limitations.
Assume a radial axis machine for terminology purposes
Magnetic flux decays with distance from the pole surface. In a multi-magnet 'real world' machine the variation is complex but a rule of thumb is that top performance 'rare earth' magnets provide a flux of ~~ 1T at half the magnet thickness out from the pole face. So eg a 6mm thick magnet with a 1mm airgap provides 1T at up to 2mm beyond the airgap. So to allow a winding to experience peak flux, winding heights radially of the order of 2 to 4mm are desirable. Peak flux is only experienced when the winding is above the magnet surface so magnet area matters. 
Here is a finite element model of flux around a magnet. North-south axis runs left-right with polesat let and right of magnet. The red line to the left of the magnet is at about 1/2 a magnet thickness from the pole face. At that point the field is about 50% of what it is at the pole face and reasonably "flat". You can see that while the flux has ABOUT halved from near maagnet face to this point, it falls much faster beyond here. Note that the number of steps in this model are too coarse to do justice to the results close to the pole face and actual flux right at face may be higher. However, alternators typically have 1 1mm or so air gap - may be higher and may be nearer 0.5mm if mechanical design and construction is very good. For typical magnet dimensions in typical small alternators (Watts to hundreds of Watts and maybe more, the very high flux area near the magnet pole face usually lies well inside the airgap and you don't get to make use of it. If magnet thicknesses are made larger compared to winding depths then this zone can extend out into winding space (which is good) but magnet cost rises and it is usually found that overall performance and cost tradeoffs do not have very large magtnet thickness to winding height ratios. 

Coils are made with wire with a finite resistance per volume - doubling wire area halves resistance but (in an ideal packing situation) halves the number of turns so halves voltage.
So -  available coil volume influences resistance. Coil thickness radially influences available field strength. Coil area influences volume. So magnet sizing ties into coil area, thickness and volume in several ways. Leading to the sad but unavoidable conclusion that bigger stronger magnets are better if power per size is the main target.
Note that in real-world applications this is not always the case. Economics often matters more than sheer performance per size. Washing machine makers who implement direct drum drive brushless DC motors (with the Fisher & Paykel (now Haier) smartdrive as a superb example) often choose to use ferrite magnets with a consequent larger coil size and so larger diamter rotor and overall machine dimensions as a consequence.
Some alternator or motor makers utilise aluminum wire (with higher resistance per area than copper (and lower mass)) due to absolute lower overall costs even after the increase in size for a given performance is takem into account.
Notes / details / comments :
Discussion is with respect to a radial flux machine just so terms match but this applies just as well to axial flux with due change to words used.
Magnetic field decays with distance from magnet pole - very rapidly relative to the sort of dimensions occupied by magnets and windings, because these are sized to optimally match cost-performance requirements. Field decays in a complex geometry related manner and due to the interaction of multiple magnets with interacting fields plus (optional) backing of magnetic material plus (optional) coil 'laminations' real device solutions are not amenable to simple numerical analysis. However, some rules of thumb can be used as starting points. Numerous finite element based programs are available to make the problems sensibly soluble. Text books say magnetic field has inverse cube law decay with distance, but that is at a significant distance relative to manet dimensions AND is due to the fact that magnet has (at least*) two poles - each with square law decay). *Magnetic monopoles are a matter for other questions :-).
In practice a rough starting point is to assume that you can get a 1T field at about half magnet radial thickness. 
Coils are made of conductors with finite resistance (based on material resistivity). This  influences the ability to fit a given number of turns within available or desired area and volume. If you have almost zero resistance nonexisteum 45 gauge wire then you can get many turns really close to the magnet surface. Nonexisteum being in vanishingly short supply,manufacturers have turned to cryogenically cooled superconductors to achieve the same effect. Despite the immense cost of providing low cryogenic temperatures and maintaining them continually (eg the electromagnet in an MRI machine is always maintained at cryogenic temperatures and is always "turned on") this is economic compared to classic alternatives, or is the only option when extremely high field strengths over extended areas or volumes are required. 

Related:
DSc thesis - DESIGN OF AXIAL-FLUX PERMANENT-MAGNET LOW-SPEED MACHINES AND PERFORMANCE COMPARISON  BETWEEN RADIAL-FLUX AND AXIAL-FLUX MACHINES
Dual stator & 
Legion
Probably diagrammatic only
http://www.researchgate.net/publication/224606165_High-speed_axial-flux_permanent-magnet_generator_with_coreless_stator
More to say but must leave - rather than delete I'll leave as is - more to say on flux in gaps, backing plates etc. 
A: This is my last question I swear. I've done a lot of research on plate backing magnets and understand how the field lines in one direction is amplified, and I have learned a lot from what you have taught me, so I don't want you to think I'm ignoring everything and trying to make up laws of the universe. But if I had the dual stator design mentioned, what effect would having smaller coils perpendicular to the ENDS of the bar magnets, in a circular configuration around the rotor have? How would that effect the electric field at the two side stators? I'm just trying to understand how different configurations effect the magnetic field and power output. Thanks a bunch.
