Ampere's law Ampere's law is the magnetic equivalent of Gauss's law. It is different in that it refers to a closed loop and the surface enclosed by it (rather than a closed surface and the volume enclosed by it, as is the case with Gauss's Law). Consider a closed loop, not necessarily a circle, which is broken into small elements of length DL_{i} with a magnetic field B_{i} at each element. The sum over elements of the component of the magnetic field along the direction of the element, times the element length, is proportional to the current I that passes through the loop. This is Ampere's law. For the case of a wire, the loop can be a circle drawn around the wire, and since the field is always tangent to the circle, cosq = 1. The circumference of the circle of radius r is 2pr, therefore Ampere's law becomes: which is the expression for the magnetic field of a wire given before. Ampere's law will also allow us to calculate the magnetic field for a solenoid. 
