# Is solenoid magnetic field formula at an axial point exactly valid?

Learning about derivation of solenoid as equivalent bar magnet I came across a step raising some doubt. The first step is to take circular element of thickness $$dx$$ and then to calculate $$B$$(the magnetic field) at the point due to this element and finally integrating. But my doubt is the derivation says that there are $$n×dx$$ turns in $$dx$$ thickness where $$n$$ is turns per unit length, but how in real world we can have a wire so thin so as to have $$n×dx$$ turns in infinitesimal length?

• We don't need to have a thin wire as $n×dx$ is infinitesimally small for any finite $n$. So we are not fitting a finite number of turns in an infinitesimal length.. – user243267 Dec 1 '19 at 8:31