A small circular loop of wire of radius 5.0 cm and resistance R = 1.3 10-3 ? is

Question

A small circular loop of wire of radius 5.0 cm and resistance R = 1.3 10-3 ? is centered inside a large circular loop of wire of radius 50 cm (see figure below). The larger loop, which initially carries a current I = 8.6 A, is cut and its current is reduced to zero over a time interval of 1.1 10-6 s. Find the average current in the smaller loop during this time interval. (The magnetic field of the larger loop is approximately constant over the smaller loop.)

Reference: http://www.webassign.net/colfunphys1/22-p-009-alt.gif

magnitude:

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Explanation / Answer

megnetic field induced by larger loop Bo = uo . I . / (2r) where: uo = permeability in vacuum = 4.phi x 1E-7 T . m / A I = loop's current = 8.6 A r = loop's radius = 5 cm so Bo = 1.080E-4 T average current in the smaller loop during time interval of 1.1x10^-6 s is i = (Bo . A/ dt) / R where R = loop's resistance = 1.3x10^-3 O A = area of the small loop = 78.54 cm2 dt = time interval = 1.1x10^-6 s so we get i = 27.57 A

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