A wire loop with an area of 2.0 m^2 and a resistance of 5.0 ohms lies flat in th

Question

A wire loop with an area of 2.0 m^2 and a resistance of 5.0 ohms lies flat in the x-y plane. A spatially uniform but time dependent magnetic field [Bx(t) = 0; By(t) = B0 sin(wt); Bz(t) = BoCos(wt); where Bo = 1.5T and w=3.0 rad/s] exists throughout the region. What is the induced current in the loop at t=2.0s? Next the loop is rotated so that it now lies in the x-z plane. What is the induced current in the loop at t=2.0s in this new orientation?. Make a diagram clearly showing the direction of the induced current in the loop at t=2.0s in each orientation

Explanation / Answer

flux = B*A = 1.5cos(wt)*2 = 3cos(3t)

E = N*dFLUX/dt = 1*3*(-sin(3t))*3 = -9sin(3t)

i = E/R = -93sin(2t)/5 =1.8 sin(3t)

direction is clockwise during the phase pi to 2pi

direction is anti clockwise during the phase 0 to pi

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