Uniformity in a solenoid I know the magnetic field strength increases as the number of turns in the solenoid increases.
However, I've learnt the field inside the solenoid is usually nearly uniform.
So, does the number of turns in the solenoid effect the uniformity of the field inside the solenoid? Does the field gets closer to uniform as the number of turns increases?
 A: If the windings in a solenoid are not closely spaced, there will be some inhomogeneity in the field - so more turns per unit length helps. Usually for "ideal" calculations one assumes a continuous sheet of current.
The second thing is the length. For a finite length magnet the field quickly drops off as you move away from the isocenter. The longer the magnet, the less the curvature of the field in the center.
This is why MRI machines have such a long bore - although the region of uniform field is usually only 50 cm or so, the bore (main magnet) is well over a meter long.
A: The expression for the magnetic field due to a long solenoid can easily be derived using Ampere's Law. The expression is $$\vec{B}=\mu_onI\hat{z}$$
where $\hat{z}$ is a unit vector pointing along the axis of the solenoid, $n$ is the number of turns per unit length, and $I$ is the current running through the solenoid. This derivation assumes that the solenoid is infinitely long so that, by symmetry, the field only points in the $\hat{z}$ direction inside the solenoid. Note that the density of the windings affects the strength of the field, not the number of windings (which in this case is infinite).
Of course, no solenoid is infinite so the longer the solenoid is, the better the above expression approximates the field of the finite solenoid. So it's the length of the solenoid affects the uniformity of the field, not necessarily the number of turns.
A: It is all relative depending on one's measurement scale. A small homogeneous area may be found in a relatively short (length) to diameter (width) solenoid but the homogeneous area will be minute and perhaps not useful or measurable as homogeneous with a 'standard' Tesla/gaussmeter probe due to the probe's relatively large sensors to a relatively small homogeneous volume.
As commented above, from some MRI description and from measurements with two teslameters earlier today, the flux density (field strength) near the 'poles' of a solenoid vary wildly as one moves between the axis and the edge of the coil.
It is similar to variances on the surface of the poles of permanent magnets measured yesterday; The flux density at the centre is weaker than at the edges. The flux density on the surface increases the closer one measures to the edge of a magnet, and decreases towards and at the centre on the pole. The magnets/solenoids I have measured to date have been up to 20mm thick (v.short) and from 75mm sq to c.100mm diameter blocks, discs and coils. Thus as Floris says, a longer relative to diameter coil could give a larger (but might still be relatively small) completely uniform (homogeneous) flux density area inside the coil.
