A conducting loop is made in the form of two squares of sides s 1 = 3.8cm and s
ID: 778695 • Letter: A
Question
A conducting loop is made in the form of two squares of sides s1 = 3.8cm and s2 = 7.9 cm as shown. At time t = 0, the loop enters a region of length L = 20.5 cm that contains a uniform magnetic field B = 1.1 T, directed in the positive z-direction. The loop continues through the region with constant speed v = 37 cm/s. The resistance of the loop is R = 1.1 .
A.) At time t = t1 = 0.034 s, what is I1, the induced current in the loop? I1 is defined to be positive if it is in the counterclockwise direction.
B.) At time t = t2 = 0.728 s, what is I2, the induced current in the loop? I2 is defined to be positive if it is in the counterclockwise direction.
C.) What is Fx(t2), the x-component of the force that must be applied to the loop to maintain its constant velocity v = 37 cm/s at t = t2 = 0.728 s?
D.) At time t = t3 = 0.588 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
A) At t = t1 = 0.034 s, small square will be inside the magnetic field.
induced emf in the loop, emf = B*v*s1
induced current, I1 = emf/R
= B*v*s1/R
= 1.1*0.37*3.8*10^-2/1.1
= 0.014 A
direction : clockwise
so, I1 = -0.014 A
B)
At t = t2 = 0.718 s, big square will be inside the magnetic field and moving out.
induced emf in the loop, emf = B*v*s2
induced current, I2 = emf/R
= B*v*s2/R
= 1.1*0.37*7.9*10^-2/1.1
= 0.0292 A
direction : counter clockwise
so, I2 = +0.0292 A
C) F(x) = B*I2*s2*sin(90)
= 1.1*0.0292*7.9*10^-2*1
= 2.53*10^-3 N
D)
At t = t3 = 0.588 s, small square will be inside the magnetic field and coming out.
induced emf in the loop, emf = B*v*s1
induced current, I3 = emf/R
= B*v*s1/R
= 1.1*0.37*3.8*10^-2/1.1
= 0.014 A
direction : counter clockwise
so, I3 = +0.014 A
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