Figure 1
The curl is a vector. It is a measure of the circulation of a vector field. The component of the curl of the vector H in the z direction normal to the surface is defined as
where , is the area of the rectangular loop lying in the xy plane shown in Figure 1.

Since the distances are small, when y changes to , the value of the x component of H changes to . Integrating H around the rectangular loop shown in Figure 1 in the counter-clockwise direction,

Dividing Equation 2 by gives the z component of the curl of H .
The x and y components of the curl are found in a similar manner.
The curl can also be expressed as a determinant.
Equation 6 is the integral form of Faraday's law.
Replacing H by E in Equation 1. Plug Equation 6 into Equation 1. Then consider a surface to be divided into many small surfaces. Apply Equation 1 to each of the small surfaces and sum over all the small surfaces. This results in the following differential form for Faraday's law,

Also, since

It follows that
Equation 9 is the differential form of Ampere's law.