# 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 $\overrightarrow{H_{o}}&space;=H_{xo}&space;\&space;\overrightarrow{a_{x}}+H_{yo}&space;\&space;\overrightarrow{a_{y}}+H_{zo}&space;\&space;\overrightarrow{a_{z}}$ .

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

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

## Author: vikramarka

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