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Unformatted text preview: Practice Midterm 2 Solution 1 Diamond Circuit a) First lets calculate electric field due to two cylinder without dielectric. Uni- formly charge inner cylinder with total charge + Q and uniformly charge outer cylinder with total charge- Q . By symmetry around z-axis, we know electric field will be pointing in r direction. That is, vector E = E r r . Drawing gaussian pill-vox around cylinder with radius r , we can use gausss law, contintegraldisplay vector E vector A = Q enc (1) integraldisplay L integraldisplay 2 E r r rrddz = + Q (2) integraldisplay L integraldisplay 2 E r rddz = Q (3) 2 LE r r = Q (4) E r = Q 2 Lr (5) vector E = Q 2 Lr r (6) We can find potential difference between two cylinder by using equation V =- integraltext vector E d vector l . V =- integraldisplay vector E d vector l (7) V b- V a =- integraldisplay b a Q 2 Lr r rdr (8) V b- V a =- integraldisplay b a Q 2 Lr dr (9) V b- V a = Q 2 L ln a b (10) Since we are interested in potential drop V a- V b = V , V = Q 2 L ln b a (11) 1 Definition of capacitance is C = Q V thus, C = 2 L ln b a (12) (You should have above expression in your equation sheet). But since there is dieletric between two cylinder C = KC = K 2 L ln b a (13) b) How to simplify capacitor is shown in Figure 1. Capacitors in series can be simplified by using relationship...
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- Spring '08