Accordingly, the efficiency of electrostatic motors decreases with decreasing scale. The absence of long conducting paths (like those in electromagnets) makes resistive losses smaller to begin with, however, and a detailed examination (Section 11.7) shows that efficiencies remain high in absolute terms for motors of submicron scale. The above relationships show that electromechanical systems cannot be scaled in the simple manner suggested for purely mechanical systems, even in the classical continuum approximation. Electromagnets are far less attractive for nanoscale systems, since
At a distance of 1 nm
from a conductor carrying a current of 10 nA, the field
strength is 2×10
are minute in nanoscale
systems: two parallel, 1 nm long segments of conductor,
separated by 1 nm and carrying 10 nA, interact with a
force of 2×10 The magnetic field energy of a nanoscale current element is small:
The scaling of inductance can be derived from the above, but is independent of assumptions regarding the scaling of currents and magnetic field strengths:
The inductance per
nanometer of length for a fictitious solenoid with a 1 nm
2 cross sectional area and one turn per nanometer of
length would be ~ 10
In systems with time-varying currents
and fields, skin-depth effects increase resistance at
high frequencies; these effects complicate scaling
relationships and are ignored here. The following
simplified relationships are included chiefly to
illustrate trends and magnitudes that For
Combining the
characteristic 17 resistance and 10 |

Copyright © 1998 by John Wiley & Sons, Inc.