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Unformatted text preview: # 2.8 " 10!4 C . Vcd # VC4 0 VC5 # V28 # 9 V and Q28 # C28V28 # 2.6 " 10!4 C . Vbd # VC5 0 VC6 # V21 # 12 V and Q21 # C21V21 # 2.5 " 10!4 C . Vbc # VC3 ! VC2 # V6 # 2.5 V and Q6 # C6V6 # 1.5 " 10!5 C . 24.74. EVALUATE:! Note that 2V72 0 V18 0 V28 # 2(7.0 V) 0 13 V 0 9 V # 36 V, as it should. IDENTIFY:! The force on one plate is due to the electric field of the other plate. The electrostatic force must be balanced by the forces from the springs. SET UP:! The electric field due to one plate is E # = 2!0 . The force exerted by a spring compressed a distance z0 ! z from equilibrium is k ( z0 ! z ) . EXECUTE:! (a) The force between the two parallel plates is F # qE # 2 q= q2 (CV ) 2 !0 A2 V 2 ! AV 2 # # #2 #0 2 . 2!0 2!0 A 2!0 A z 2!0 A 2z (b) When V # 0, the separation is just z0 . When V R 0 , the total force from the four springs must equal the !0 AV 2 ! AV 2 and 2 z 3 ! 2 z 3 z0 0 0 #0. 2 2z 4k (c) For A # 0.300 m 2 , z0 # 1.2 " 10!3 m , k # 25 N/m and V # 120 V , so 2z 3 ! (2.4 " 10!3 m)z 2 0 3.82 " 10!10 m3 # 0 . The physical solutions to this equation are z # 0.537 mm and 1.014 mm. EVALUATE:! (d) Stable equilibrium occurs if a slight displacement from equilibrium yields a force back toward the equilibrium point. If one evaluates the forces at small displacements from the equilibrium positions above, the 1.014 mm separation is seen to be stable, but not the 0.537 mm separation. electrostatic force calculated in part (a). F4 springs # 4k ( z0 ! z ) # Capacitance and Dielectrics 24.75. 24-25 IDENTIFY:! The system can be considered to be two capacitors in parallel, one with plate area L( L ! x ) and air between the plates and one with area Lx and dielectric filling the space between the plates. K! A SET UP:! C # 0 for a parallel-plate capacitor with plate area A. d ! !L EXECUTE:! (a) C # 0 (( L ! x) L 0 xKL) # 0 ( L 0 ( K ! 1) x ) D D !0 L !L 2 1 (b) dU # 2 ( dC )V , where C # C0 0 (! dx 0 dxK ) , with C0 # 0 ( L 0 ( K ! 1) x ) . This gi...
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This document was uploaded on 03/11/2014 for the course PHYSICS 240 at University of Michigan.

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