What are the limits of validity for the magnetic field of a solenoid? 1) The field outside a solenoid is approximated to be zero, because of opposites points "cancelling out". Does this approximation of the field being almost zero become worse as the diameter of the solenoid increases? (since the opposite sides are further apart) I'm looking for an answer for two cases: 1) Only the diameter increases, but all other dimensions remain the same. 2) All dimensions increase proportionally, keeping the aspect ratio the same. 
2) Are solenoids approximated as a series of perfect circles (since opposite sides cancel only in a circle)? And consequently shouldn't a stretched out solenoid's field be completely different since its nothing like a series of circles?
EDIT:

The field at P is the superposition of the fields from the opposite "points". If the diameter of the solenoid increases, the bottom "points" are further away from $P$, so their contribution to the field decreases. Therefore the assumption that the fields from the top points cancel with the bottom points becomes falser/less valid.
 A: Mostly, yes on both counts.


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*It depends whether the solenoid also gets longer as it gets wider. The approximation that the field outside the solenoid vanishes is valid for points whose distance to the solenoid's centre is much smaller than the distance to both ends. This is impossible for a point outside a solenoid that's wider than it is tall.
To answer your more specific question about opposite points, the reason these points still cancel is because there is more current per unit angle as the solenoid gets wider if the distance remains fixed. It's more complicated than this - the field really vanishes because of the cancellation of the complete integral over the infinite surface - but one good picture to keep in mind is the following.


*The field of a solenoid that's considerably stretched, or of a series of circles that are widely separated, is indeed different to that of an 'ideal' solenoid, which is usually modelled as a surface current, with no interruptions, over a cylinder. For a real solenoid with spacings between the loop, the approximation will hold for points whose distance to the nearest point on the solenoid is greater than the inter-loop spacings.
