A conducting loop is made in the form of two squares of sides s 1 = 3.8cm and s

Question

A conducting loop is made in the form of two squares of sides s1 = 3.8cm and s2 = 6.5 cm as shown. At time t = 0, the loop enters a region of length L = 19.1 cm that contains a uniform magnetic field B = 1.7 T, directed in the positive z-direction. The loop continues through the region with constant speed v = 39 cm/s. The resistance of the loop is R = 1.2 ?.

A conducting loop is made in the form of two squares of sides s1 = 3.8cm and s2 = 6.5 cm as shown. At time t = 0, the loop enters a region of length L = 19.1 cm that contains a uniform magnetic field B = 1.7 T, directed in the positive z-direction. The loop continues through the region with constant speed v = 39 cm/s. The resistance of the loop is R = 1.2 ?. 1)At time t = t3 = 0.522 s, what is I3, the induced current in the loop? I3 is defined to be positive if it is in the counterclockwise direction.

Explanation / Answer

total moving length =L+s1+s2=28.4cm

time=D/v= 28.4/40 =0.71s

At t=0.035s , the distance is 1.4 cm w
distance=velocity.time = 40.(0.035) = 1.4cm

this distance we can take as entering length of the loop.
For L=1.4cm, Area at time(dA/dt) = L*W = 1.4(3.8)cm^2 = 5.32*10^-4 m^2

e.m.f in the loop of this area:
e=-B.dA/dt=1.2*5.32*10^-4 v = 6.384 *10^-4 v
the induced current at this time i=e/R = 6.384*10^-4/2.8 (R=2.8 ohm given) = 0.228 mA

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