1. Home
2. Illustrations
3. #27

IllustrationFourth Maxwell equation: Constant electric current generates B-field

Share — copy and redistribute the material in any medium or format

Adapt — remix, transform, and build upon the material for any purpose, even commercially.

This illustration is free to use with indication of the copyright: universaldenker.org

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).