Campo magnético de un solenoide

Consider a solenoid with closely packed turns of wire so that its total length is greater than its radius.

A steady current flowing through this solenoid generates a magnetic field, which can be estimated by considering a rectangular Amperian loop through it. 

Applying Ampere's Law, the sum of the line integral of the magnetic field along each loop path equals the permeability multiplied by the net current enclosed by the loop.

Now, the magnetic field integral along path one is the product of the magnetic field and the loop length. It is zero along paths two and four since the magnetic field is perpendicular to the path. As the magnetic field outside the solenoid is zero, the integral along path three is also null.

The net enclosed current is equal to the total turns inside the Amperian loop, multiplied by the current flowing through the solenoid.

Thus, the magnetic field inside a solenoid parallel to the solenoid axis is directly proportional to the number of turns per unit length and the current.