Two of Maxwell's equations contain a path integral on the left side and an area integral on the right.Suppose the area is the surface of a piece of paper at which you are looking and is chosen to point toward you.Then, the path integral is:

Question

Quizplus · Accepted Answer

The path integral is counterclockwise around the circumference of the paper because the area integral is pointing toward you. This is because the right-hand side of Maxwell's equations is the divergence of the left-hand side, and the divergence of a vector field is a measure of how much the vector field is spreading out. In this case, the vector field is the magnetic field, and the divergence of the magnetic field is zero. This means that the magnetic field is not spreading out, and therefore the path integral must be counterclockwise around the circumference of the paper.

Two of Maxwell's Equations Contain a Path Integral on the Left