A conducting loop is made in the form of two squares of sides s 1 = 2.8cm and s

Question

A conducting loop is made in the form of two squares of sides s1 = 2.8cm and s2 = 7.3 cm as shown. At time t = 0, the loop enters a region of length L = 17.9 cm that contains a uniform magnetic field B = 1.4 T, directed in the positive z-direction. The loop continues through the region with constant speed v = 55 cm/s. The resistance of the loop is R = 1.2 ?.

Q: At time t = t3 = 0.342 s, what is I3, the induced current in the loop? I3 is defined to be positive if it is in the counterclockwise direction.

A conducting loop is made in the form of two squares of sides s1 = 2.8cm and s2 = 7.3 cm as shown. At time t = 0, the loop enters a region of length L = 17.9 cm that contains a uniform magnetic field B = 1.4 T, directed in the positive z-direction. The loop continues through the region with constant speed v = 55 cm/s. The resistance of the loop is R = 1.2 ?. At time t = t3 = 0.342 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

at t=0.342s , the the distance travelled by the loop

dis tnace= velocity.time
=55(0.342)
=18.81cm
the total distance =17.9+2.8+7.3 = 28 cm
travelled distance=18.81 cm
remaining distance=9.19cm
this should be taken as length of the loop enteraining
l=9.19 cm
breadth remains same b=7.3 cm
the area associated with this loop at this given time(dA/dt) =l.b
=7.3(9.19)
=67.087 cm^2
= 67.087*10^-4 m^2
the induced e.m.f in the loop at this time is given by,
e=-B.dA/dt
=1.4(67.087*10^-4) v
=93.9218 *10^-4 v

the induced current in this loop at this time is given by,

i=e/R
=93.9218*10^-4/1.2
=7.826mA

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