A large circular loop of 127 turns and radius of 47.0 cm carries a current of 14

Question

A large circular loop of 127 turns and radius of 47.0 cm carries a current of 14 A. A small square loop of 38 turns and 2.00 cm on a side is placed at the center of the large loop. both loops lie in the same plane. we want to find the EMF induced in the small loop if the current in the large loop increases to 45 A in 0.0370 s.

What is the initial agnetic field at the center of the large loop?

what is the magnetic field at the center of the large loop at the end of the 0.0370 seconds?

what is the magnitude of the induced EMF in the small loop?

Explanation / Answer

magnetic field due to larger loop is B =    N uoi/2R

inital magnetic field at the centre

B = 4pie-7 *127 * 14/(2*0.47)

B = 2.37 mTesla
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dB /dt = 127 * 4pi e-7 * (45-14)/(2* 0.47)*0.037)

dB/dt = 0.1421 T/s

so now

induced emf in smaller loop = emf = N A dB/dt

emf e = 38 * 0.02*0.02* 0.1421

emf e = 2.159 mV
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