# Magnetic flux threading a metal ring varies with time

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The magnetic flux threading a metal ring varies with time t according to 3at^3-bt^2, with a = 7.7s^-3m^2T, and b = 2.8 s^-2m^2T. The resistance of the ring is 2.3 Ohms. Determine the maximum current induced in the ring during the interval from t1 = -2.3 s to t2 = 7.3 s. Answer in units of A

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#### Solution Preview

flux (f) = 3at^3 - bt^2

<br>a = 7.7 SI unit

<br>b = 2.8 SI unit

<br>=> f = 3*7.7*t^3 - 2.8*t^2 = 23.1*t^3 - 2.8*t^2

<br>df/dt = 23.1*3*t^2 - 2.8*2*t

<br>=> df/dt = 46.2*t^2 - 5.6*t

<br>because ...

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