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Ampère's Circuital Law

$\displaystyle \mathbf {\nabla } \times \mathbf {B} =\mu _{0}\mathbf {J} $

An electric current creates a magnetic field around it. This phenomenon is used in motors, transformers and complex machines like MRI.

Integral form: $\oint _{C}\mathbf {B} \cdot \mathrm {d} {\boldsymbol {l}}=\mu _{0}\iint _{S}\mathbf {J} \cdot \mathrm {d} \mathbf {S} =\mu _{0}I_{\mathrm {enc} }$

Ampère's law tells us that the total magnetic field circulation around a closed loop (left-hand side of the equation) is directly proportional to the total electric current enclosed by that loop (right-hand side of the equation), with the constant of proportionality being μ0.


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