Ampere's law allows us to write
down a single equation that describes all of the ways that
electric current can make magnetic field.
But, just as with Gauss's law, this single equation is very difficult to solve.
Ampere's law says: The path integral of 
around any
(imaginary) closed path is equal to the current enclosed by the path, multiplied
by 
:
The little circle on the integral sign reminds us that the integral must be taken around a closed path. To decide whether a particular current is enclosed by the path or not, imagine stretching a thin membrane over the path, like a drumhead, so that the edge of the membrane is along the path If a current pierces the membrane, it is an enclosed current. Currents that do not pierce the membrane are left out of Ampere's law, just as charges outside of the closed surface were left out of Gauss's law. Like the charges in Gauss's law, these enclosed currents are either positive or negative. Here is the rule for deciding whether an enclosed current is positive or negative. Curl the fingers of your right hand in the direction of integration around the path. If a current pierces the membrane stretched across the loop in the direction of your thumb, then it is a positive enclosed current. If a current pierces the membrane in the opposite direction, it is negative.
When we discussed Gauss's law, we noted that the law was true no matter how distorted the surface or how complicated the electric field. Similarly, Ampere's law is always true, no matter how distorted the path or how complicated the magnetic field. In most cases, however, even though Ampere's law is true, it is useless because it is impossible to perform the path integral. In a few special, symmetric situations, however, it is easy to perform the path integral and we can obtain formulas for B that would be quite difficult to derive with the Biot-Savart law.