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by T-A
2910 days ago
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Eq. (14) is just the expression for a dipole. Keep reading to see the full solution in the simplest case (circular plates), Eq. (19). Since you insist: your derivation goes wrong right at the start by, as you say, "ignoring curvature effects", i.e. by considering radial distance only. By doing that, you are effectively imposing spherical symmetry; you are not doing parallel plates, you are doing concentric spherical shells. That makes the whole exercise pointless, since it's obvious from symmetry alone that such a device could never produce a net thrust: there is no preferred direction for the thrust to act along. To answer your final question, just look at Eq. (19): make the plate radius (R) larger. That answer should also be perfectly obvious from the limit case of infinite plates. A correct derivation for the general case must reproduce that result in that limit. Yours does the opposite; it gets worse the larger you make the capacitor. In the infinite limit, it is infinitely wrong. |
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You're also right that all that is moot from sheathing. But an ion still begins it's journey out at the bottom of a large potential well; one which is particularly steep because of the debye length, but still just as deep.