PHY 213 - Known as physics 2

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Concepts for Chapter 16: Capacitance If a potential difference is placed across two parallel conducting plate (e.g., by connecting the plates to two opposite terminals of a battery with a wire), free electrons will move through the wire from lower to higher potential (toward the + terminal and away from the – terminal of the battery) For the connection shown in the illustration to the right, the top plate will gain a positive e charge (due to a loss of electrons), while the bottom plate will gain a negative charge (due to a gain of electrons). Δ V Note, however, that no electrons will flow from e the lower plate directly to the upper plate due to e the presence of an insulating gap between the two plates. As the charges accumulate on the plates, an E-field is generated within the connecting wire that opposes a loss of electrons from the upper plate and a gain of electrons by the lower plate. At some point the opposing E-field will become sufficiently strong that any additional transfer of electrons from the upper to the lower plate will be prevented. Here the electric force “pushing” an electron onto the lower plate will be equal in magnitude to the electric force “pushing” an electron back off of the lower plate. Consequently, an equilibrium state will develop wherein the loss in potential energy (PE) resulting from one additional electron being “pushed” onto the bottom plate ( | Δ PE | = q ⋅Δ V battery ) will be exactly offset by the gain in PE resulting from one electron being “pushed” back off of the bottom plate ( | Δ PE | = q ⋅Δ V , where ⋅Δ V = the potential difference across the two parallel plates at equilibrium). q ⋅Δ V battery = q ⋅Δ V Δ V = Δ V battery That is, charge will continue to accumulate on the two plates until the potential difference across the plates is equal to the potential difference (potential drop) across the battery. Since the E-field is a conservative field, the potential difference that develops across the parallel plates as a result of the transfer of electrons from the upper to the lower plate is independent of the path along which these electrons are transferred. Consequently, the potential difference across the plates, Δ V, is the same as if the electrons were being transferred along a path from the upper to the lower plate directly across the gap between the plates. If the gap between the plates is d, the difference in potential (the potential drop) across the two
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This note was uploaded on 08/25/2009 for the course PHY 213 taught by Professor Cao during the Summer '08 term at Kentucky.

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PHY 213 - Known as physics 2

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