11. (a) Ohm’s law combines with Faraday’s law to give i = − N R d Φ B dt where R is the resistance of the coil. In this case, N = 1 (it is a single loop), and we integrate to ±nd the charge: Z t0 idt = − 1 R Z t0 d Φ B dt dt q ( t )= − 1 R (Φ B ( t ) − Φ B (0)) which is equivalent to the expression shown in the problem statement. We have used little more than the fundamental theorem of calculus; no particular assumptions have been made about how the integrations should be performed. The result is independent of the way ~
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