Explain Sign Convention for Ampere�S Law

Sign convention:

Fold ur Right hand fingers along the integration path, then the erect thumb gives the +ve current direction. If no of current are passing through the surface bounded by the closed path then the ampere’s law can be written as

\(\begin{array}{l}oint{overrightarrow{Bcenterdot }overrightarrow{dell }}={{mu }_{o}}({{I}_{net}})\end{array} \)
. Where Inet = I1 – I2 – I3 + I4 …

The magnetic field

\(\begin{array}{l}overrightarrow{B}\end{array} \)
written in the integral is not only contributed by the currents linked with the closed path but also the current which are not linked with the closed path, But
\(\begin{array}{l}oint{overrightarrow{B}centerdot overrightarrow{dell }}\end{array} \)
is contributed only by the currents which are linked with the path.

Note:- In gauss law of electrostatics, we are relating the normal component of

\(\begin{array}{l}overrightarrow{E}\end{array} \)
with the net charge which is enclosed in the closed surface ‘s’. But in ampere’s law, we are relating the tangential component of
\(\begin{array}{l}overrightarrow{B}\end{array} \)
over a closed path with the net current linked by that path.

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