Quick question about the flux density through a solenoid.

[rock.freak667]

Homework Statement

the flux density through a solenoid is given by

$$B=\mu_o n I$$

Where n is the number of turns per unit length.

The number of field lines per unit area is proportional to B.

I am assuming that at or near the centre of the solenoid the number of field lines per unit area decreases so B decreases.
If that is true, then how come the formula stated above doesn't account for distance from the centre of the solenoid?

 

[Snazzy]

That's not the flux through a solenoid, that's the magnetic field strength. The magnetic field is uniform inside the solenoid (like how a parallel-plate capacitor has a uniform electric field between the two plates).

 

[rock.freak667]

Magnet flux density is the same as field strength?

The reason I ask is that there is a question in which a Hall probe measures tehe magnetic flux density in a solenoid. They take measurements fromt the centre of the solenoid(x=0cm) until the end of the solenoid(x=16cm).
The results showed that as the x increases, B decreased.
Then the question asked "What conclusions can be made about the (i) the region where the formula ($B=\mu_0 n I$ applies"