Capacitance - PHY2061 Enriched Physics 2 Lecture Notes...

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PHY2061 Enriched Physics 2 Lecture Notes Capacitance Capacitance Disclaimer: These lecture notes are not meant to replace the course textbook. The content may be incomplete. Some topics may be unclear. These notes are only meant to be a study aid and a supplement to your own notes. Please report any inaccuracies to the professor. +q q A set of conductors can store electric charge. The net charge Q =0= q q , but the magnitude of charge on each conductor is | q |. This charge q is proportional to the potential difference between the conductors: qCV VV V V qC V +− Δ= − ≡ = The constant of proportionality between charge and potential difference is C capacitance. Unit is Farad (F) Coulomb/Volt. 6 12 1F = 1 0 F 1pF = 10 F μ To set up a potential difference between 2 conductors requires an electric “pump”, such as a battery (see next chapter). C Δ V + +q q A larger capacitance implies that a large charge q is stored for the same potential difference V . Capacitance depends only on the geometry of the conductors, not the charge q or voltage V . We can see this through examples. D. Acosta Page 1 9/26/2006
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PHY2061 Enriched Physics 2 Lecture Notes Capacitance Parallel Plate Capacitor Δ V + d A Consider the top view of the 2 plates: E Create a Gaussian surface (box) that extends inside and outside one of the conductor surfaces. Gauss’ Law enc 0 S q d ε ⇒Φ= = EA v 0 = E inside a conductor 0 d ⋅= on left/right edges 0 E on front outside face only enc 0 0 S q dE A qE A = = ⇒= v The electric potential difference between the 2 plates is given by: + E ds opposite directions VVV d d d s Vd V d + +− Δ= − = − ⋅ ⋅ = Δ= Δ Es Es E E E So for parallel plates: 00 0 2 12 2 C 8.85 10 8.85 pF/m Nm VA Δ A A V dd qCV A C d εε ⎛⎞ == = Δ ⎜⎟ ⎝⎠ = × = D. Acosta Page 2 9/26/2006
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PHY2061 Enriched Physics 2 Lecture Notes Capacitance Cylindrical Capacitor (Cable) Let inner conductor have radius a , and outer radius b .
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This note was uploaded on 05/19/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

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Capacitance - PHY2061 Enriched Physics 2 Lecture Notes...

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