. A MPERE ’ S C IRCUITAL L AW There is an alternative and appealing way in which the Biot-Savart law may be expressed. Ampere’s circuital law considers an open surface with a boundary (Fig. .
). The surface has current passing through it. We consider the boundary to be made up of a number of small line elements. Consider one such element of length dl.
We take the value of the tangential component of the magnetic field, B t , at this element and multiply it by the length of that element dl [Note: B t dl= B . d l ]. All such products are added together. We consider the limit as the lengths of elements get smaller and their number gets larger.
The sum then tends to an integral. Ampere’s law states that this integral is equal to µ times the total current passing through the surface, i.e., I µ