# Formula 4. Maxwell Equation of Electrostatics in Integral Form Magnetic field Electric current Vacuum permeability

## 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

`$$ L $$`Unit

`$$ $$`

A closed loop (e.g. a circle) along which the magnetic field \(B\) is summed up by means of the line integral.

Here \( \text{d}\boldsymbol{l} \) is a small line element of the loop. The direction of \(\text{d}\boldsymbol{l}\) points tangential to the loop at each point on the loop.

## Electric current

`$$ I $$`Unit

`$$ \mathrm{A} $$`

Electric current enclosed by the loop \(L\).

## Vacuum permeability

`$$ \mu_0 $$`Unit

`$$ \frac{\mathrm{Vs}}{\mathrm{Am}} = \frac{ \mathrm{kg} \, \mathrm{m} }{ \mathrm{A}^2 \, \mathrm{s}^2 } $$`

The vacuum permeability is a physical constant and has the following experimentally determined value:

`$$ \mu_0 ~=~ 1.256 \, 637 \, 062 \, 12 ~\cdot~ 10^{-6} \, \frac{\mathrm{Vs}}{\mathrm{Am}} $$`