Formula 4. Maxwell Equation of Electrostatics in Integral Form Magnetic field Electric current Vacuum permeability
$$\oint_{S} \class{violet}{\boldsymbol{B}} ~\cdot~ \text{d}\boldsymbol{s} ~=~ \mu_0 \, \class{red}{I}$$
Magnetic field
$$ \class{violet}{\boldsymbol{B}} $$ Unit $$ \mathrm{T} $$ Magnetic flux density determines the force on a moving electric charge.
Maxwell's fourth equation of electrostatics states that an electric current \(I\) causes a rotating magnetic field \(B\) and vice versa.
Closed loop
$$ S $$ A closed loop (e.g. a circle) along which the magnetic field \(B\) is summed up by means of the line integral.
Here \( \text{d}\boldsymbol{s} \) is a small line element of the loop. The direction of \(\text{d}\boldsymbol{s}\) points tangential to the loop at each point on the loop.
Electric current
$$ \class{red}{I} $$ Unit $$ \mathrm{A} $$ Electric current enclosed by the loop \(S\).
Vacuum permeability
$$ \mu_0 $$ Unit $$ \frac{\mathrm{Vs}}{\mathrm{Am}} = \frac{ \mathrm{kg} \, \mathrm{m} }{ \mathrm{A}^2 \, \mathrm{s}^2 } $$ Magnetic field constant is a physical constant and occurs whenever electromagnetic fields are involved. It has the value: \( \mu_0 = 1.256 \cdot 10^{-6} \, \frac{ \text{N} }{ \text{A}^2 } \).