Page 233 - Mechanics of Microelectromechanical Systems
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220 Chapter 4
where and are the direct inductances of the two coils and is the
mutual inductance connecting the two coils. These inductances are:
It can be shown that in the case where is constant over the equivalent coil,
the force of Eq. (4.81) reduces – as shown in Seely and Poularikos [8] – to:
Another way of calculating the interaction force between the coil and the
magnet of Fig. 4.38 (a) is by expressing the magnetic-electromagnetic energy
in a different fashion, namely:
where R is the magnetic reluctance of the portion of magnetic line
comprising the coil, air gap and magnet, and which is calculated as:
If there was no magnetic core inside the coil, then is zero in the equation
above. By applying the definition of Eq. (4.81), the interaction force
becomes:
Example 4.9
A circular coil of radius is placed at the end of a microcantilever, as
shown in Fig. 4.35. A magnet defined by its area thickness and
inductance is fixed under the coil, such that an air gap is formed
between the magnet and the coil. Determine the current of the coil that will
