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

Formula: 4. Maxwell Equation of Magnetostatics (Differential Form)
Current Generates Rotating Magnetic Field

Magnetic field

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

Curl field

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

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

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