Field at Center of Current Loop

The form of the magnetic field from a current element in the BiotSavart law becomes
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

The current used in the calculation above is the total current, so for a coil of N turns, the current used is Ni where i is the current supplied to the coil.
The Earth's magnetic field at the surface is about 0.5 Gauss.
Discussion of current loop

Index
Magnetic field concepts
Currents as magnetic sources 