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Unformatted text preview: Physics 54 Electrostatics 3 Always remember that you're unique, just like everyone else. Bumper Sticker Storing energy in the E-feld Like other forms of potential energy, electrostatic potential energy is stored in the sense that it can be recovered and converted into kinetic energy or other forms. A device designed speciFcally to store energy in the electrostatic Feld is called a capacitor , and its effectiveness in storing energy is measured by its capacitance . We will analyze capacitors, especially those of simple geometry. We will Fnd that the energy stored can be thought of as distributed through space, with an amount per unit volume proportional to the squared magnitude of the E-Feld. This suggests that wherever there is an E-Feld there is stored energy. This will be an important insight in our later discussion of the electromagnetic Feld. Capacitance Capacitors store electrostatic energy by separating electric charges. or this purpose they usually consist of a pair of conductors on which equal and opposite charges are placed. The conductors are isolated so that the charges cannot cancel. The resulting E- Feld causes a difference in potential between the two conductors. Capacitance measures the ratio of the charge to this potential difference: Capacitance Let two conductors carrying charges + Q and Q be arranged so that the potential difference between them is V . This system has capacitance C = Q / V . In fact, V will be proportional to Q , so C actually depends only on the geometric arrangement and the electric properties of any non-conductors that might be present. One of the simplest geometric arrangements is a pair of at parallel plate conductors, with dimensions large compared to the spatial separation between them. PHY 54 1 Electrostatics 3 We can use the infnite sheet approximation to obtain the E-feld From Gauss's law. In that approximation we fnd that the felds oF the oppositely charged plates cancel except in the region between them, where the feld is E = 4 k = 4 kQ / A ....
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