Quantitatively answer the following questions regarding scaling and miniaturization
(a) Electrostatic scaling: prove that electrostatic force between the two plates of a charged capacitor is a surface force (~L2); How about the stored energy under constant voltage on the capacitor (~L1, ~L2, or ~L3)? What is the breakdown electric field in air? How does this breakdown field scale with dimensions?
(b) How about piezoelectric force scaling (does the force act like that of capacitive elements, i.e. piezoelectric force is a surface force?)
(c) Build a mathematical model of an electrostatic rotary motor, and discuss scaling in force, torque and power. Is friction a surface force? Does the friction scale along with power generated by the electrostatic micromotor?
(d) Thermal scaling: why heat transfer in micro world is fast? Is this property good for actuators and heat sinks?