Magnetic Field in a Single Current Coil

[opsb]

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.
Thanks.

 

[cragar]

Did you try the biot-savart law ? It might work

 

[opsb]

I did, but you get this really tricky integral. I was wondering if there might be a smarter way to do it than brute force.

 

[torquil]

When you run into a difficult integral: just use it to define a function and name it after yourself!

Although in this case it seems to be elliptic integrals, which are already taken :-)

Did you get the same as this?:

http://www.netdenizen.com/emagnet/offaxis/iloopoffaxis.htm"