Ampère-Maxwell Law

Just as Faraday’s Law shows how a changing Magnetic Field can cause Induced Electric Fields, the Ampère-Maxwell Law demonstrates how a changing Electric Field can induce a Magnetic Field.

Definition §

Ampère-Maxwell's Law

$$\oint \vec{B}\cdot d\vec{l}={\mu }_0\left(I_{enclosed}+{ϵ}_0\frac{\text{d}{\Phi }_E}{\text{d}t}\right)$$

Note

• $\vec{B}$ = Magnetic Field (in $T$)
• $\vec{l}$ = Path vector of the loop. $d\vec{l}$ returns an infinitesimally small section of said path.
• ${\mu }_0$ = Permeability of free space
• ${ϵ}_0$ = Permittivity of free space
• $I_{enclosed}$ = Current enclosed inside the loop.
• $\frac{\text{d}{\Phi }_E}{\text{d}t}$ = Change in Electric Flux
• $\oint$ = Line integral

Implications §

The second half of the equation (${\mu }_0{ϵ}_0\frac{\text{d}{\Phi }_E}{\text{d}t}$) gives the magnetic field from a changing electrical flux…