Explain and State Ampere�S Law With Equation

In case of Electric field we used gauss’s law to calculate the electric field for highly symmetric charge distributions; a similar law exists in magnetism, it is ampere’s law its states that:

\(\begin{array}{l}\oint{\overrightarrow{B}\centerdot \overrightarrow{\nabla }}={{\mu }_{o}}{{I}_{enclosed}}\end{array} \)

The left hand side of ampere’s law
\(\begin{array}{l}\oint{(Bcos \theta )\nabla }\end{array} \)
means the sum up of the component of magnetic field B along the closed path length
\(\begin{array}{l}\nabla\end{array} \)
. In order to apply ampere’s law we consider a symmetrical closed curve around the current carrying wire (amperian loop).

The right side of equation is the net current enclosed within the closed path

\(\begin{array}{l}\oint{\nabla }\end{array} \)

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