1_9 - PHY 5346 HW Set 2 Solutions Kimel 3. 1.9 I will be...

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Unformatted text preview: PHY 5346 HW Set 2 Solutions Kimel 3. 1.9 I will be using the principle of virtual work. In the figure below, Fl is the work done by an external force. If F is along l (ie. is positive), then the force between the plates is attractive. This work goes into increasing the electrostatic energy carried by the electric field and into forcing charge into the battery holding the plates at constant potential 12 . Conservation of energy gives Fl W Q 12 or F From problem 1.8, a) Charge fixed. 1) Parallel plate capacitor W 1 2 2 dQ 12 , 12 0A A 0 d W 1 2 0A dQ A 0 2 W l Q 12 l d d Q2 2 0A Q2 Q 0, F W (attractive) 2 0A l l 2) Parallel cylinder capacitor 12 ln d , a a 1 a 2 a 0 Q W 1 Q 12 F W 1Q ln d 1 (attractive) a 0 2 2 2 0d l d b) Potential fixed 1) Parallel plate capacitor Using Gauss's law, Q 12 A d 0 , l Q 12 A d2 0 2 2 A 2 F 1 0 A 12 12 2 0 1 0 A 12 1 0 A 2 2 2 d2 d2 d 2) Parallel cylinder capacitor L W 1 Q 12 , and Q 0 d 12 2 ln a so L 2 W 1 0 d 12 , 2 ln a Q l F 1 2 0L Qd 0A 2 2 d 1 Q2 2 0A W l 0L 1 2 0L 2 12 2 d ln a d 12 ln 2 d d a 2 12 1 2 ln 2 d d a 0L 2 12 ln 2 d d a 0L 2 12 ln 2 d d a ...
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