Lateral electric fields in a lateral electrostatic actuator

[cgiustini]

Hello,

I'm reading through section 6.2.2 of https://ocw.mit.edu/courses/electri...s-spring-2009/readings/MIT6_013S09_chap06.pdf on page 157. I understand all the math, but I have a conceptual questions that I don't seem to be able to answer myself:

The paragraph under equation 6.2.11 mentions electric pressure differences across the capacitor plates that are responsible for pushing the plates apart laterally. However, previous parts of the text talk about capacitor plate overlap and ignoring fringing fields, suggesting that we are only concerned with the electric field in the overlapping region, which in my mind should always be normal to the plates if we are making that simplification. In my mind, my two previous sentences contradict each other. Can anyone explain what I may be missing? Where does the lateral force originate from if we are only concerned with the simplified capacitor made up of the overlapping parts of the plates?

Thanks,
Carlo

 

[berkeman]

I only skimmed the text, but the figure sure looks like the plates are not overlapping much where they want the forces to be generated. Do you have any other references about these types of devices?

 

[cgiustini]

Hi,

Thank you for looking in this. I found an additional text here: https://books.google.com/books?id=N...VAhVEw1QKHRfaAW8Q6AEITzAI#v=onepage&q&f=false. Page 177 shows a similar overlapping static actuator, and it essentially shows the same information.

In both sets of notes, the force applied to the moving plate of the overlapping actuator is calculated by calculating the derivative of the total energy in the overlapping capacitor/battery system (which changes as a function of the plate moving and overlapping capacitance increasing). Because the plate moves laterally, the force in question (an electric force because the only energy present is electric) must be lateral as well. However, it seems like the capacitance that is used in the energy equations is only made up of the overlapping parts of the actuator. This fundamentally seems oversimplified to me as I would expect the lateral electric forces to be driven by forces between charges that are not right on top of each other (ie, not in overlapping parts of the capacitor). Any thoughts as to why it may not be such an oversimplification?

Also one more theoretical question: is a force always being applied to something if its energy changes with distance? It seems to be the case if one calculates force as the derivative of energy with respect to distance. It seems a bit counter-intuitive at first, but maybe it is just a new concept to me.

Thanks,
Carlo