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Unformatted text preview: is a property of the object!! (concentric cylinders here) • Assume some Q (i.e., +Q on one conductor and –Q on the other) • These charges create E field in region between conductors • This E field determines a potential difference V between the conductors • V should be proportional to Q; the ratio Q/V is the capacitance. 33 cross-section a4 a3 Calculation Calculation A capacitor is constructed from two conducting cylindrical shells of radii a1, a2, a3, and a4 and length L (L >> ai). a2 a1 metal metal What is the capacitance C of this capacitor ? C≡ Q V • Strategic Analysis: – – – – Put +Q on outer shell and –Q on inner shell Cylindrical symmetry: Use Gauss’ Law to calculate E everywhere Integrate E to get V Take ratio Q/V: should get expression only using geometric parameters (ai, L) Note: Many of you email me and ask “prof—what equation should I use for homework problem 3?” I say: Ppttuy, yukk! Never ask which equation! Ask what concepts should I apply and equations say: will become obvious. will Calculation Calculation cross-section +Q A capacitor is constructed from two conducting cylindrical BB shells of radii a1, a2, a3, and a4 and length L (L >> ai). + + + + + + + ­Q + + + + + metal + + + What is the capacitance C of this capacitor ? + a2 a1 + a4 a3 + C≡ + Q V metal Where is +Q on outer conductor located? (A) at r=a4 (B) at r=a3 (C) both surfaces (D) throughout shell Why? Gauss’ law: Q dA ∫ Eg = ε enclosed Q 0 enclosed =0 We know that E = 0 in conductor (between a3 and a...
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