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Formula 4th Maxwell Equation in Integral Form Magnetic field    Electric current    Electric field   

Formula: 4th Maxwell Equation in Integral Form
Current + time-dependent E-field generate a rotating B-field and vice versa
E-field change generates B-field

Magnetic field

The magnetic flux density indicates how strong the magnetic field is at a certain location \((x,y,z)\) and in which direction it points.

Closed line

Line (e.g. a current-carrying conductor) over which you integrate. It is the edge of the surface \( A \) (for example the edge of a circle). The line must be closed, i.e. its beginning and its end must be connected.


This surface is enclosed by the closed loop \(L\). This can be, for example, the area of a circle.

Electric current

Electric current running along the line \(L\).

Electric field

Electric field tells what would be the electric force on a sample charge at a given location \((x,y,z)\) if that sample charge is placed at that location.

Here the E-field is differentiated with respect to time: \( \frac{\partial \boldsymbol{E}}{\partial t} \).

Vacuum permeability

Magnetic field constant is a natural constant and occurs in the description of electromagnetic phenomena. It is: \( \mu_0 ~=~ 4\pi \cdot 10^{-7} \, \frac{\text N}{\text{A}^2} \).