1. Home
2. Illustrations
3. #24

# IllustrationSecond Maxwell equation in integral form

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

Maxwell equation for the divergence of the magnetic field $$\nabla \cdot \boldsymbol{B}$$. This Maxwell equation states that there are no magnetic monopoles. Magnetic fields always occur as dipoles with a south pole S and a north pole N. Thus the divergence of the magnetic field or the flux integral is always zero:$\nabla \cdot \boldsymbol{B} ~=~ 0$or equivalently: $\oint_{A} \boldsymbol{B} ~\cdot~ \text{d}\boldsymbol{a} ~=~ 0$

The scalar product $$\boldsymbol{B} ~\cdot~ \text{d}\boldsymbol{a}$$ only picks out the component $$\boldsymbol{B}_{||}$$ of the magnetic field $$\boldsymbol{B}$$ that is parallel to the $$\text{d}\boldsymbol{a}$$ element.