# Formula 4. Maxwell Equation of Magnetostatics (Differential Form) Magnetic field    Current density

## Magnetic field

Unit
Magnetic flux density determines the magnitude and direction of the magnetic force on a moving electric charge.

## Curl field

Unit
Vector magnetic curl field as cross product between the nabla operator $$\nabla$$ and the magnetic field $$\boldsymbol{B}$$:$\nabla \times \boldsymbol{B} ~=~ \begin{bmatrix} \frac{\partial B_z}{\partial y} - \frac{\partial B_y}{\partial z} \\ \frac{\partial B_x}{\partial z} - \frac{\partial B_z}{\partial x} \\ \frac{\partial B_y}{\partial x} - \frac{\partial B_x}{\partial y} \end{bmatrix}$

Das Rotationsfeld $$\nabla \times \boldsymbol{B}(x,y,z)$$ ist ein Vektorfeld, das angibt, wie stark das Magnetfeld $$\boldsymbol{B}$$ am Ort $$(x,y,z)$$ rotiert.

## Current density

Unit
Electric current density indicates the electric current per cross-sectional area. According to Maxwell's equation, an electric current generates a magnetic curl field around the current (magnetostatics). In the case of a time-varying B-field, a time-varying E-field is also generated.

## Vacuum permeability

Unit
The vacuum permeability is a physical constant and has the following experimentally determined value:$$\mu_0 ~=~ 1.256 \, 637 \, 062 \, 12 ~\cdot~ 10^{-6} \, \frac{\mathrm{Vs}}{\mathrm{Am}}$$