In cases with a high degree of symmetry, Ampere's Law may be used much more easily.
In general, it is equal to the curl of the vector potential, which means its own divergence is zero. Its value for a given distribution of source currents can be calculated by integrating the Biot-Savart [BEE-oh sah-VAR] Law. In cases with a high degree of symmetry, Ampere's Law may be used much more easily. FTP, name this vector field usually symbolized by a capital B, whose value at the earth's surface is about 40 Gauss and pointing north.
In general, it is equal to the curl of the vector potential, which means its own divergence is zero.
{Magnetic} field (prompt on B field)