For this problem, you need to determine the magnetic field at the center of the

Question

For this problem, you need to determine the magnetic field at the center of the large loop. The formula for that is 8 - where R is the radius of the loop. 2R A small circular loop of wire of radius 5.0 cm and resistance R 1.3 x 10 3 ls centered inside a large circular loop of wire of radius 50 cm see figure below). The larger loop, whichinitially carries a clockwise current ! = 6.7 A, is cut and its current is reduced to zero over a time interval of 1.2 x 10-6 s. Find the voltage & current in the smaller loop during this time interval. (The B-field of the larger loop is approximately constant over the smaller loop.) current direction Select

Explanation / Answer

magnetic field at the center of loop B = uo*I/(2*R)

magnetic flux through the smaller loop, phi_1 = B*A = B*pi*r^2 = uo*I*pi*r^2/(2*R)

after the curretn is made zero

magneitc flux through th e smaller loop, phi_2 = 0

induced emf = rate of change in flux = -(phi2 - phi1)/t

emf = uo*I*pi*r^2/(2*R*t)

emf = (4*pi*10^-7*6.7*pi*0.05^2)/(2*0.5*1.2*10^-6)

emf = 0.055 v

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current i = emf/R = 0.055/(1.3*10^-3) = 42.3 A

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