## Dr. Ahmed G. Abo-Khalil

Electrical Engineering Department

## field Depiction

$abla imes mathbf{B} = mu_0mathbf{J}$

assuming quasi-static conditions, i.e.

$frac{partial E}{partial t} ightarrow 0,quad abla imes mathbf{A} = mathbf{B} ,,$

the lines and contours of A relate to B like the lines and contours of B relate to j. Thus, a depiction of the A field around a loop of B flux (as would be produced in a toroidal inductor) is qualitatively the same as the B field around a loop of current.

The figure to the right is an artist's depiction of the A field. The thicker lines indicate paths of higher average intensity (shorter paths have higher intensity so that the path integral is the same). The lines are drawn to (aesthetically) impart the general look of the A-field.

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