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Unformatted text preview: C2 / N + m 2 / # 1.63 " 10!5 C/m 2 EVALUATE:! We could also calculate = directly as Q/A. = # 24.4. Q 0.148 " 10 !6 C # # 1.63 " 10 !5 C/m 2 , which checks. A 9.08 " 10!3 m 2 A when there is air between the plates. d A # (3.0 " 10!2 m) 2 is the area of each plate. IDENTIFY:! C # !0 SET UP:! (8.854 " 10 !12 F/m)(3.0 " 10 !2 m) 2 # 1.59 " 10 !12 F # 1.59 pF 5.0 " 10!3 m EVALUATE:! C increases when A increases and C increases when d decreases. !A Q IDENTIFY:! C # . C# 0 . Vab d SET UP:! When the capacitor is connected to the battery, Vab # 12.0 V . EXECUTE:! C # 24.5. EXECUTE:! (a) Q # CVab # (10.0 " 10!6 F)(12.0 V) # 1.20 " 10!4 C # 120 $ C (b) When d is doubled C is halved, so Q is halved. Q # 60 $ C . (c) If r is doubled, A increases by a factor of 4. C increases by a factor of 4 and Q increases by a factor of 4. Q # 480 $ C. EVALUATE:! When the plates are moved apart, less charge on the plates is required to produce the same potential difference. With the separation of the plates constant, the electric field must remain constant to produce the same potential difference. The electric field depends on the surface charge density, = . To produce the same = , more charge is required when the area increases. 24-1 24-2 24.6. 24.7. Chapter 24 IDENTIFY:! C # Q !A . C# 0 . Vab d SET UP:! When the capacitor is connected to the battery, enough charge flows onto the plates to make Vab # 12.0 V. EXECUTE:! (a) 12.0 V Q (b) (i) When d is doubled, C is halved. Vab # and Q is constant, so V doubles. V # 24.0 V . C (ii) When r is doubled, A increases by a factor of 4. V decreases by a factor of 4 and V # 3.0 V . EVALUATE:! The electric field between the plates is E # Q / !0 A . Vab # Ed . When d is doubled E is unchanged and V doubles. When A is increased by a factor of 4, E decreases by a factor of 4 so V decreases by a factor of 4. !A IDENTIFY:! C # 0 . Solve for d. d SET UP:! Estimate r # 1.0 cm . A # , r 2 . ! , r 2 !0, (0.010 m)2 !0 A # # 2.8 mm . so d # 0 C d...
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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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