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# ch25_p45 - 45(a The electric field in the region between...

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45. (a) The electric field in the region between the plates is given by E = V / d , where V is the potential difference between the plates and d is the plate separation. The capacitance is given by C = κε 0 A / d , where A is the plate area and κ is the dielectric constant, so 0 / d A C κε = and E VC A = = × × × = × κε 0 12 12 4 2 4 50 100 10 54 885 10 100 10 10 10 V F F m m V m b gc h c hc h . . . . (b) The free charge on the plates is q f = CV = (100 × 10 –12 F)(50 V) = 5.0 × 10 –9 C. (c) The electric field is produced by both the free and induced charge. Since the field of a large uniform layer of charge is q /2 ε 0 A , the field between the plates is E q A q A q A q A f f i i = + 2 2 2 2 0 0 0 0 ε ε ε ε , where the first term is due to the positive free charge on one plate, the second is due to
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