The curl is a vector. It is a measure of the circulation of a vector field. The component of
the curl of the vector
direction normal to the surface
is defined as
where , is the area of the rectangular
loop lying in the
plane shown in Figure 1.
Since the distances are small, when
the value of the
around the rectangular loop shown in Figure 1 in the counter-clockwise direction,
Dividing Equation 2 by
component of the curl of
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,
It follows that
Equation 9 is the differential form of Ampere's law.