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Unformatted text preview: 8.02 Sample Final B Solutions (Modified from Spring 1994) p. 1/3 1. Capacitor (a) The energy stored is in the electric field. Since E is nearly constant we can just multiply the energy density by the volume inside the capacitor: R r d P E 2 2 2 2 2 2 E d R d R E V u U E E = = = (b) With the electric field increasing, we have a d d E isplacement current: ( ) dt dE r B dt dE r I r B dl B dt dE r dt r E d dt I nt displaceme nt displaceme 2 2 2 2 1 2 = = = = = = = Since the displacement current is up, the B field is out of the page at P. (c) dt rE dt r E S 2 2 = = = dE dE B E 1 1 1 G G G (to the right/inwards!) (d) To find the total energy flowing in consider that the band at r = R has an area A = 2 Rd , so ( ) ( ) dt dE R Rd dt RE A R r S dt 2 2 dE dE dU 2 1 = = = = G G . Notice that this is indeed the time derivative of U E that we calculated in part (a)....
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This note was uploaded on 04/27/2009 for the course 8 8.02 taught by Professor Hudson during the Spring '07 term at MIT.
- Spring '07