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216 Chapter 4
Figure 4.35 Microcantilever for Lorentz-based magnetic field detection
Solution:
The interaction between the external field B and the current in the
circular loop will tend to rotate the loop about an axis that is perpendicular to
the length direction and passes through the loop’s center. The value of this
moment is given in Eq. (4.65). It can be shown that application of this
moment will produce a slope at the microcantilever’s tip according to:
By combining Eqs. (4.65) and (4.69), the external field becomes:
where the inertia moment of the microcantilever’s cross-section is:
4.2 Magnetic Transduction
The principle of magnetic actuation/sensing is similar to the one defining
the electromagnetic-based operation. A magnet that is placed in an external
magnetic field will be acted upon or will sense forces/moments that result
from the interaction between the own magnetic field of the magnet and the
external magnetic field. Figure 4.36 (a) illustrates a short magnet of length l
(which is pictured as a vector departing from the south pole S and arriving at
the north pole N of the magnet), together with the field lines that go
externally from the N pole and close in the S pole. Similar to a loop carrying
a current I, a magnetic dipole moment m can be defined in the form:
