By dividing x out of both sides of the last equation, one finds: The magnetic field inside a solenoid is proportional to both the applied current and the number of turns per unit length. There is no dependence on the diameter of the solenoid...
Equation 8.1. Apply the path integral to the rectangular loop a b c d in Figure 8.3, far from either end where B is uniform inside the solenoid and almost zero outside it. University Physics II, Exp 8: Magnetic Field of a Solenoid.
We can find the magnetic field due to a solenoid carrying a steady current as follows.
In the above expression for the magnetic field B, n is the number of turns per unit length, sometimes called the "turns density". The expression is an idealization to an infinite length solenoid, but provides a good approximation to the field of a long solenoid.
However, magnetic fields are three dimensional and so it is helpful to use a picture to visualize the field and the current that causes it. In addition, when you use partially-solved equations (such as the definition of the magnetic field due to a solenoid)...
Since we are dealing with a long solenoid, all of the components of the magnetic field not pointing upwards cancel out by symmetry.
2. Study the magnetic field strength inside and around a toroid, a circular-shaped solenoid. 3. If you have studied calculus, refer to a calculus-based physics text to see how the equation for the field of a solenoid can be derived from Ampere’s law.
Use the magnetic field sensor to measure the strength of the magnetic field at various points inside the solenoid.
7 Magnetic field inside a long thin solenoid. 8 references.
For a lab we need the equation of the magnetic field strength produced by a solenoid a distance r away from it (outside of it). I tried looking online and couldn't find one that didn't involve a bunch of cross products or similar.