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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
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 ?
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
will become obvious.
+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
∫ Eg =
ε enclosed Q 0 enclosed =0 We know that E = 0 in conductor (between a3 and a...
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This document was uploaded on 02/13/2014.
- Spring '14