Question

At a square coil ofside 2d and resistance R is placed in an external perpendicular time dependent uniform magnetic field of magnitude Bet(t) = Bok te kt where Bo and k are constants Ext(t) 2d 2d (a) Sketch a graph of Bext(t). (b) There will be a time-dependent induced current in the coil, i(t). Is there a time when this induced current will be zero? If so, when? If not, why not? (c) If we take a counterclockwise current, when viewed from above the square, to be pos tive and a clockwise current to be negative, make a rough sketch of i).(d) Derive a formula for i(t), and double-check that it qualitatively agrees with your sketch (e) At t0, calculate the magnetic field Bside created by one side of the current-carrying (f) Calculate the total magnetic field created by the current-carrying loopat 0, Binduced. (g) You will notice that we completely ignored Binduced when we calculated the induced from part (c) loop. Which direction does it point? current in part (d), even though it is also time-dependent! Was that a reasonable thing to do? (Hint: compare Binduced with a representative value of the external field, say Bo) (By the way, when we make this approximation, what we are saying is that the self-inductance of the square loop is negligible.)

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