Differential form of Ampere’s Circuit law

Consider a closed rectangular path in xy-plane which encloses a current element and the current flows in z-direction.

\overrightarrow{H}  at  center point P  is \overrightarrow{H_{o}} =H_{xo} \ \overrightarrow{a_{x}}+H_{yo} \ \overrightarrow{a_{y}}+H_{zo} \ \overrightarrow{a_{z}} .

By applying Gauss’s law to differential volume  element leads to a concept of divergence as similar to that by applying ampere’s law to a current element in a  closed path leads to curl.

from ampere’s circuit law 

\oint \overrightarrow{H} . \overrightarrow{dl}= \overrightarrow{H}_{1-2}.\overrightarrow{\Delta l}_{1-2}+\overrightarrow{H}_{2-3}.\overrightarrow{\Delta l}_{2-3}+\overrightarrow{H}_{3-4}.\overrightarrow{\Delta l}_{3-4}+\overrightarrow{H}_{4-1}.\overrightarrow{\Delta l}_{4-1}.



Author: vikramarka

Completed M.Tech in Digital Electronics and Communication Systems and currently working as a faculty.