Deadline: 100% until Thursday, April 6 at 11:59 PM Time Dependent Current in a W
ID: 1555081 • Letter: D
Question
Deadline:
100% until Thursday, April 6 at 11:59 PM
Time Dependent Current in a Wire
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An infinite straight wire carries a current I that varies with time as shown above. It increases from 0 at t = 0 to a maximum value I1 = 2.6 A at t = t1 = 12 s, remains constant at this value until t = t2 when it decreases linearly to a value I4 = -2.6 A at t = t4 = 26 s, passing through zero at t = t3 = 21.5 s. A conducting loop with sides W = 27 cm and L = 51 cm is fixed in the x-y plane at a distance d = 44 cm from the wire as shown.
1)
What is the magnitude of the magnetic flux through the loop at time t = t1 = 12 s?
T-m2
Your submissions:
1.08*10^-7
Computed value:
1.08E-07
Submitted:
Wednesday, April 5 at 2:33 PM
Feedback:
Your answer has been judged correct; the exact answer is: 1.08064090978592 × 10-7.
2)
What is 1, the induced emf in the loop at time t = 6 s? Define the emf to be positive if the induced current in the loop is clockwise and negative if the current is counter-clockwise.
V
Your submissions:
2.34*10^-8
Computed value:
2.34E-08
Submitted:
Wednesday, April 5 at 2:33 PM
Feedback:
3)
What is 2, the induced emf in the loop at time t = 14 s? Define the emf to be positive if the induced current in the loop is clockwise and negative if the current is counter-clockwise.
V
Your submissions:
0
Computed value:
0
Submitted:
Wednesday, April 5 at 2:34 PM
Feedback:
Correct!
4)
What is the direction of the induced current in the loop at time t = t3 = 21.5 seconds?
Clockwise
Counterclockwise
There is no induced current at t = t3
5)
What is 4, the induced emf in the loop at time t = 23.75 s? Define the emf to be positive if the induced current in the loop is clockwise and negative if the current is counter-clockwise.
V
1 W -------r----+-- t----- 1 0 4 d y!Explanation / Answer
1) What is the magnitude of the magnetic flux ? through the loop at time t = t1= 12.0 s?
= B.dA = (i/2x)(w.dx) = iw/2 (1/x)dx
integration from d to d+L
= iw/2 ln((d+L)/(d))
= i (4*3.14e-7*0.27/2*3.14)* ln((0.51+0.44)/(0.44))
= i * 4.156e-8
= 2.6 * 4.156e-8
= 1.08e-7 Wb
2) What is 1, the induced emf in the loop at time t = 6 s? Define the emf to be positive if the induced
current in the loop is clockwise and negative if the current is counter-clockwise.
= d = dt = 4.4154e-8 -(di/dt) = 4.156e-8 * -(2.6/12) = -9e-9 V
Counterclockwise
3) What is 2, the induced emf in the loop at time t = 14.0 s? Define the emf to be positive if the induced current in the loop is clockwise and negative if the current is counter-clockwise.
= 0 V
4) The direction of induced emf acts always opposite to the applied magnetic field and thus magnetic flux. In this case at t = 21.5 s the current is zero. Hence there is no change in induced emf and so the direction of induced emf is as previous. So the direction is counter clock wise
5) What is 4, the induced emf in the loop at time t = 23.75 s? Define the emf to be positive if the induced current in the loop is clockwise and negative if the current is counter-clockwise.
= d = dt = 4.4154e-8 (di/dt) = 4.4154e-8 * (2.6/4.5) = +2.55e-8 V
clockwise
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