Prozorov_05

# Prozorov_05 - PHYSICS 222 Introduction to Classical Physics...

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PHYSICS 222 Introduction to Classical Physics II Prof. Ruslan Prozorov Iowa State University Fall 2011 LECTURE 5 Capacitance and capacitors. Dielectrics. Electric field energy.

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keep charges apart and you get capacitance 31 August 2011 PHYS222 - Prof. Ruslan Prozorov - Iowa State University 2
capacitance 31 August 2011 PHYS222 - Prof. Ruslan Prozorov - Iowa State University 3 remember from previous lecture: 0 V d Capacitance is defined as: - only geometry! 0 Q A C V d

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capacitor 31 August 2011 PHYS222 - Prof. Ruslan Prozorov - Iowa State University 4 0 A Q V C V d With the same potential difference - store more charge if capacitance is larger
capacitors of different geometry: sphere 31 August 2011 PHYS222 - Prof. Ruslan Prozorov - Iowa State University 5 0 Q A C V d use the definition: look at the Gaussian surface between the shells. From Gauss’s law, electric field between the shells is:   2 0 1 4 Q E r r  Electric potential between the shells is: 2 0 0 1 1 4 4 b b a a r r a b r r Q dr Q V Edr r r r   so, the capacitance is: 0 4 a b b a r r Q C V r r 

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cylindrical capacitor 31 August 2011 PHYS222 - Prof. Ruslan Prozorov - Iowa State University 6 0 1 2 E r  0 0 ln 2 2 b b a a r r b a r r r dr Q V Edr r L r   so, the capacitance is: 0 2 ln b a Q C r V r 