4 a a a4 3g71032g71

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Unformatted text preview: (c) , C # 4, !0 R , as in Problem (24.67). 2C 8, !0 R IDENTIFY:! We model the earth as a spherical capacitor. rr SET UP:! The capacitance of the earth is C # 4, !0 a b and, the charge on it is Q = CV, and its stored energy is rb ! ra U # 1 CV 2 . 2 EXECUTE:! (a) C # . 6.38 "106 m / . 6.45 "106 m / # 6.5 "10!2 F 1 9.00 " 109 N + m 2 /C2 6.45 " 106 m ! 6.38 " 106 m (b) Q # CV # . 6.54 " 10!2 F / (350,000 V) = 2.3 " 104 C (c) U # 1 CV 2 # 1 . 6.54 " 10!2 F / (350,000 V)2 # 4.0 " 109 J 2 2 EVALUATE:! While the capacitance of the earth is larger than ordinary laboratory capacitors, capacitors much larger than this, such as 1 F, are readily available. 24-22 Chapter 24 24.70. IDENTIFY:! The electric field energy density is u # 1 !0 E 2 . U # 2 SET UP:! For this charge distribution, E # 0 for r 1 ra , E # Example 24.4 shows that Q2 . 2C 8 for ra 1 r 1 rb and E # 0 for r 5 rb . 2, !0 r U 2, !0 for a cylindrical capacitor. # L ln( rb / ra ) 2 %8& 82 EXECUTE:! (a) u # 1 !0 E 2 # 1 !0 ' (# 2 2 2 2 ) 2, !0 r * 8, !0 r r (b) U # H udV # 2, L H urdr # U 82 L8 2 b dr and # ln(rb / ra ) . L 4, !0 4, !0 rH r a Q2 Q2 8 2L # ln(rb / ra ) # ln(rb / ra ) . This agrees with the result of part (b). 2C 4, !0 L 4, !0 Q2 EVALUATE:! We could have used the results of part (b) and U # to calculate U / L and would obtain the same 2C result as in Example 24.4. IDENTIFY:! C # Q / V , so we need to calculate the effect of the dielectrics on the potential difference between the plates. SET UP:! Let the potential of the positive plate be Va , the potential of the negative plate be Vc , and the potential (c) Using Equation (24.9), U # 24.71. midway between the plates where the dielectrics meet be Vb , as shown in Figure 24.71. C# Q Q # . Va ! Vc Vac Vac # Vab 0 Vbc . Figure 24.71 EXECUTE:! The electric field in the absence of any dielectric is E0 # reduced to E1 # E2 # Q . In the first dielectric the electric field is !0 A E0 Q Qd %d & # and Vab # E...
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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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