742_Physics ProblemsTechnical Physics

742_Physics ProblemsTechnical Physics - 82 Capacitance and...

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82 Capacitance and Dielectrics P26.10 With θπ = , the plates are out of mesh and the overlap area is zero. With θ = 0 , the overlap area is that of a semi-circle, π R 2 2 . By proportion, the effective area of a single sheet of charge is πθ af R 2 2 When there are two plates in each comb, the number of adjoining sheets of positive and negative charge is 3, as shown in the sketch. When there are N plates on each comb, the number of parallel capacitors is 21 N and the total capacitance is FIG. P26.10 CN A NR d d =− = −∈ − = 2 2 0 0 2 0 2 a f a f a f a f a f effective distance . P26.11 (a) C k e b a == × = A 2 50 0 2 8 99 10 268 9 727 258 ln . .l n . . . ch ej nF (b) Method 1: Vk b a e = F H G I K J 2 λ ln × × F H G I K J = q V A 810 10 162 10 2 8 99 10 1 62 10 302 6 7 97 . . .. l n . . . C 50.0 m Cm kV e j Method 2: V Q C × × = 268 10 6 9 . . . k V P26.12 Let the radii be b and a with ba = 2 . Put charge Q on the inner conductor and –Q on the outer. Electric field exists only in the volume between them. The potential of the inner sphere is
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