b. Derive an expression for the magnitude of the induced emf in the loop as a function of time for the interval t = 0 s to t = 6 s. c. Calculate the magnitude of the induced current at time t = 3 s. d. Sketch a graph of the induced current in the loop as a function of time from t = 0 s to t = 18 s. Show the direction of the induced current on the loop depicted in the Figure above.
b. Derive an expression for the magnitude of the induced emf in the loop as a function of time for the interval t = 0 s to t = 6 s. c. Calculate the magnitude of the induced current at time t = 3 s. d. Sketch a graph of the induced current in the loop as a function of time from t = 0 s to t = 18 s. Show the direction of the induced current on the loop depicted in the Figure above.
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b. Derive an expression for the magnitude of the induced emf in the loop as a function of time for the interval t = 0 s to t = 6 s.
c. Calculate the magnitude of the induced current at time t = 3 s.
d. Sketch a graph of the induced current in the loop as a function of time from t = 0 s to t = 18 s. Show the direction of the induced current on the loop depicted in the Figure above.
e. Calculate the total energy dissipated in the loop during the first 6 seconds.
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t [s]
12
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20
A circular loop of area 0.26 m2 and resistance R = 1.65 $ lies in the plane of the page/screen as shown. A magnetic field with constant direction but varying magnitude is perpendicular to the plane of the loop as depicted in the
Figure above. The time dependence of the magnetic field strength in shown in the graph below. (Hint: The graph has four distinct regions/time intervals. The equation for the first portion is given on the graph. During the second time
interval the magnetic field strength is constant. In the third region the field decreases linearly to zero and stays at zero for the last time interval.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac048e26-edc8-46ba-8829-c16c07a7a6b4%2F9371191b-8dd9-4c80-8ecd-8394ff6e7bbe%2Fmkt8kjd_processed.png&w=3840&q=75)
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B [T]
3.00
2.50
2.00
1.50
1.00
0.50
0.00
0
2
В = 2.0e
2.0 e-0.25 t
6
8
10
t [s]
12
14
16
18
20
A circular loop of area 0.26 m2 and resistance R = 1.65 $ lies in the plane of the page/screen as shown. A magnetic field with constant direction but varying magnitude is perpendicular to the plane of the loop as depicted in the
Figure above. The time dependence of the magnetic field strength in shown in the graph below. (Hint: The graph has four distinct regions/time intervals. The equation for the first portion is given on the graph. During the second time
interval the magnetic field strength is constant. In the third region the field decreases linearly to zero and stays at zero for the last time interval.)
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Step 1: Concepts used:
VIEWStep 2: (b) Find the expression for the induced emf in the given time interval:
VIEWStep 3: (c) Find the magnitude of the induced current at the given instant:
VIEWStep 4: Find the expression for the induced current in the loop:
VIEWStep 5: (d) Draw the graph between induced current and the time in the given time interval.
VIEWStep 6: (d) Draw the direction of the loop:
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