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

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:

Quizplus · Accepted Answer

One of the equations is Faraday's Law, which states that the path integral of the electric field around a closed loop is equal to the negative of the time rate of change of the magnetic flux through any surface bounded by the loop. Since the magnetic field is pointing towards you, the flux through the paper is increasing (since it is moving towards you), so the time rate of change of the flux is positive. Therefore, the path integral must be counterclockwise to produce a negative result, which matches the right side of the equation.

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