I am considering the equivilence between Biot-Savart's Law and Ampere's Law for a current loop. The form of the magnetic field from a current element in the Biot-Savart law becomes dB = [tex]\mu[/tex]oI dL sin[tex]\theta[/tex]/4[tex]\pi[/tex]r2 which in this case simplifies greatly because the angle =90 ° for all points along the path and the distance to the field point is constant. The integral becomes B = [tex]\mu[/tex]oI/2r It would appear that there is sufficient symmetry to apply Ampere's Law, with the line integral [tex]\oint[/tex] B dL cos [tex]\theta[/tex] = [tex]\mu[/tex]oI of the enclosed value B dL cos [tex]\theta[/tex] reflecting the surface area of a torus. However, as I work this out I cannot get the same value as produced by Biot-Savart's Law. Is the problem that the B Field is not constant such that the line integral [tex]\oint[/tex] B dL cos [tex]\theta[/tex] cannot be easily calculated?