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Unformatted text preview: stant by ! # K !0 . The maximum voltage is E0 = # , where K K !0 = is the surface charge density on each plate. The induced surface charge density on the surface of the dielectric is given by = i # = (1 ! 1/ K ) . SET UP:! From Table 24.2, for polystyrene K # 2.6 and the dielectric strength (maximum allowed electric field) is 2 " 107 V/m . EXECUTE:! (a)! ! # K !0 # (2.6)!0 # 2.3 " 10!11 C2 N + m 2 related to the maximum possible electric field before dielectric breakdown by Vmax # Emax d . E # (b) Vmax # Emax d # (2.0 " 107 V m)(2.0 " 10!3 m) # 4.0 " 104 V (c) E # % ) = K !0 and = # !E # (2.3 " 10!11 C2 /N + m2 )(2.0 " 107 V/m) # 0.46 " 10!3 C/m2 . 1& * = i # = '1 ! ( # (0.46 " 10!3 C/m 2 )(1 ! 1/ 2.6) # 2.8 " 10!4 C/m 2 . K EVALUATE:! The net surface charge density is = net # = ! = i # 1.8 " 10!4 C/m 2 and the electric field between the plates is E # = net / !0 . 24-12 Chapter 24 24.44. IDENTIFY:! C # Q / V . C # KC0 . V # Ed . SET UP:! Table 24.1 gives K # 3.1 for mylar. EXECUTE:! (a) BQ # Q ! Q0 # ( K ! 1)Q0 # ( K ! 1)C0V0 # (2.1)(2.5 " 10!7 F)(12 V) # 6.3 " 10!6 C . 24.45. (b) = i # = (1 ! 1/ K ) so Qi # Q(1 ! 1/K ) # (9.3 " 10!6 C)(1 ! 1/ 3.1) # 6.3 " 10!6 C . (c) The addition of the mylar doesn’t affect the electric field since the induced charge cancels the additional charge drawn to the plates. EVALUATE:! E # V / d and V is constant so E doesn't change when the dielectric is inserted. (a) IDENTIFY and SET UP:! Since the capacitor remains connected to the power supply the potential difference doesn’t change when the dielectric is inserted. Use Eq.(24.9) to calculate V and combine it with Eq.(24.12) to obtain a relation between the stored energies and the dielectric constant and use this to calculate K. EXECUTE:! Before the dielectric is inserted U 0 # 1 C0V 2 so V # 2 2 .1.85 " 10!5 J / 2U 0 # # 10.1 V C0 360 " 10!9 F (b) K # C/C0 U 0 # 1 C0V 2 , U # 1 CV 2 so C/C0 #...
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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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