2.4 Coupling 'Magnetic Field - Mechanical Field'

Due to the movement of the voice coil and the aluminum former in the magnetic field the so-called motional emf-term (electromotive force term)

 

$$\gamma\vec{v}\times(\nabla \times \vec{A})$$ (7)

has to be added to equation (6). This term represents the induced eddy current density in an electrically conductive body moving with velocity $\vec{v}$ in a magnetic field. Here, the velocity $\vec{v}$ is given as the time derivative of the mechanical displacement $\vec{d}$

 

$$\vec{v}=\partial\vec{d}/\partial t .$$ (8)

A further coupling between the mechanical and the magnetic field is due to the magnetic volume force $\vec{f}_\mathrm{V}$ resulting from the interaction between the magnetic field and the total electric currents in the conductive parts of the moving coil system. This force can be expressed as

 

$$\vec{f}_\mathrm{V} \vec{J} \times \vec{B}$$ =

$$\left(-\gamma \frac{\partial \vec{A}}{\partial t} - \gamma \nabla V + \gamma \vec{v} \times (\nabla \times \vec{A}) \right)$$ =

$${}\times(\nabla\times\vec{A}),$$ (9)

where $\vec{J}$ denotes the total electric current density.