Main Question or Discussion Point
I understand that the magnetic field in a solenoid can be approximated as being constant as the length of the solenoid tends to infinity, but I was wondering if anyone could show me or point me in the direction of a derivation of the precise magnetic field at any point within a single loop of current. The magnetic field at any point along an axis perpendicular to the coil running through its centre can be determined, is there a solution to the field at any point in the plane of the coil. I wrote the problem down and got an integral that looked pretty hard, and I couldn't figure out a way to solve it. Any help would be appreciated.