A square loop has side lengths of 10.0 cm and lies in the xy-plane, with its bot

Question

A square loop has side lengths of 10.0 cm and lies in the xy-plane, with its bottom left comer at the origin. A magnetic field is acting parallel to the 2-axis represented by the equation B = 0.900y^2t. If the resistance in the loop is 0.900 Ohm, what is the induced current in the loop at t = 0.900 s? The figure provided shows a switch that has been in position 1 for a long time. If it is changed to position 2 at t = 0 s, what is the first time at which the current is maximum? J = 4-50 mH, C = 15.1 muF, V =3.52 V and R = 3.60 Ohm.

Explanation / Answer

total magnetic flux phi = integral B*A = integral(0.9y^2*x*t*dy) = 0.9*x*t*y^3/3 = 0.3*x*y^3*t

induced emf = rate of change in flux

emf = 0.3*x*y^3

emf = 0.3*0.1*0.1^3 = 3*10^-5 V

current I = emf/R = 3*10^-5/0.9 = 3.33*10^-5 A

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In LC oscillation circuit

i = Imax*sin(wt)

w = 1/sqrt(LC) = 1/sqrt(4.5*10^-3*15.1*10^-6) = 3836.23 /s

for i = Imax

1 = sin(3836.23*t)

t = 0.41 ms <<<<<<----------answer

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