Hi dears
I'm going to design an electrostatically suspended mass system and I need to know the kinetics for calculating the amount of voltage that needs to apply on electrodes on top and below of the mass to create an electric field and suspending the mass.
please help me as soon as possible
we have an undergraduate experiment in atomic lab. called Rutherford experiment about an oil drop suspend in the air using electrostatics force, so you can use the same idea. best regards
First, of course, all depends on the charge contained in this mass you're trying to suspend. We'll call it q.
I'd begin with the Lorentz force:
F = q(E + v X B)
If the mass is to be suspended, stationary, then you won't have any magnetic v X B force acting on it, and you're left with F = qE.
The weight of the mass is F = mg, where F is the force of gravity, g is 9.8 m/sec^2, acting on the mass. So to keep this mass suspended, you must have the case
qE = mg, and therefore
E = mg/q
So this is the electric field required to keep that mass m, with charge q, suspended. Assuming, naturally, that we are talking about "at the surface of the earth," or otherwise you'd have to enter some other value of g.
Now to figure out the relationship between voltage between two very large plates (large compared to the size of the mass) and the electric field this voltage generates:
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elewor.html
E * d = delta V, where d is the distance between the plates and delta V is the potential difference between the plates.
Last step, substituting,
delta V = (mg/q) * d
Albert Manfredi's post is the answer to the question.
I would only add that if the mass is not point-like, if it has a volume, then there is also an Archimedian force which pushes the mass upwards. This force is equal in absolute value to the weight of the displaced amount of air.
The point charge approach presented above by Albert has to be corrected for the design of real experiment. For instance, consider a tiny solid gold sphere (radius, r =1mm) suspended between the parallel plates of capacitor separated by a distance d=1cm in the air. As it stems from electrostatics, the tiny gold sphere initially located on the lower plate of capacitor at U=0 (applied voltage across the capacitor) will hover over the plate at about U=27 kV. The charge of hovering gold sphere turns out to be about 300 pC. This experiment is dаngerous due to 30 kV/cm breakdown voltage for air. However, this experiment can be performed using a tiny iron sphere, which will hover at the lower voltage across the capacitor, about U=17 kV. The required voltages were calculated according to the expression U=d*sqrt[rρg/(3ε0)], where ρ is the density of tiny sphere, ε0 is the permittivity of free space.
tanks a lot for your guide
all of them were useful for me. but I have some problems yet. I'm trying to design an electrostatically suspended MEMS structure and I want to know is it possible to apply such this ultra high voltage for utilizing sensor in micro scale dimension?
and if so, how we can use this system in implantable bio-medical applications?
Shahab, the micro size of suspended object (m,r) decreases the required voltage across the capacitor according to the formula above but creates big problems with a charge (q) of micro object.
However, your sentence: "electrostatic suspended MEMS structure applicable for biomedicine" sounds odd for me, because a charged object can be suspended in the electrostatic field only for zero resultant force acting on it. The counteracting force in case of Albert and my examples above was gravitation force which, I guess, is not so effective in implantable biomedicine.
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