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Illustration Fourth Maxwell equation: Constant electric current generates B-field

Fourth Maxwell equation: Constant electric current generates B-field
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A constant electric current \(I\) through a surface \(A\) generates a time-independent magnetic field \( \boldsymbol{B} \) which forms a vortex along the edge \(L\) of the surface. This experimental finding can be summarized in the following 4th Maxwell equation in integral form:\[ \oint_{L} \boldsymbol{B} ~\cdot~ \text{d} \boldsymbol{l} ~=~ \mu_0 \, I \]

This is the special case of the fourth Maxwell equation, when the electric field is time-independent (electrostatics, Ampere's law).