Formula: 2. Maxwell equation (differential form) Magnetic field
$$\nabla \cdot \class{violet}{\boldsymbol{B}} ~=~ 0$$
Magnetic field
$$ \class{violet}{\boldsymbol{B}} $$
Magnetic flux density determines the magnitude and direction of the magnetic force on a moving electric charge.
Divergence field
$$ \nabla \cdot \class{violet}{\boldsymbol{B}} $$
Scalar divergence field is the scalar product between the nabla operator \(\nabla\) and the magnetic field \( \boldsymbol{B} \):
\[ \nabla \cdot \class{violet}{\boldsymbol{B}} ~=~ \frac{\partial \class{violet}{B_{\text x}}}{\partial x} + \frac{\partial \class{violet}{B_{\text y}}}{\partial y} + \frac{\partial \class{violet}{B_{\text z}}}{\partial z} \]
The divergence field is no longer a vector field but a scalar function. The divergence field \( \nabla \cdot \class{violet}{\boldsymbol{B}(x,y,z)} \) at the location \((x,y,z)\) is always zero. This means that there are no magnetic charges.