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4. Microtransduction: actuation and sensing 219
where is the magnetic field created by the magnet, is the magnet area
normal to the field and is the permeability of the free space.
4.3 Magnetic-Electromagnetic Transduction
Several MEMS applications use the interaction between the
electromagnetic and magnetic fields in order to enhance the transduction
capabilities. Combining a coil carrying a current with a permanent magnet,
such that their fields are parallel, is an example where a force is generated
along the two fields’ directions. This force and the microsystem’s geometry
are illustrated in Fig. 4.38 (a).
There are two different ways to calculate the force between the two
components. One method is to transform the real magnet into an equivalent
coil, as sketched in Fig. 4.38 (b), based on the fact that the magnet and the
equivalent coil have the same magnetic moment m, which leads to the
equation:
The interaction force can be calculated as the partial derivative of the total
magnetic-electromagnetic energy in terms of direction as:
Figure 4.38 Magnetic-electromagnetic interaction: (a) Coil and permanent magnet; (b)
Equivalent coil-coil
The magnetic energy can be calculated as the sum:
