
(a)
The maximum emf induced between the ends of the conductor.
(a)

Answer to Problem 46P
The maximum emf induced between the ends of the conductor is
Explanation of Solution
Write the expression to obtain the magnetic flux.
Here,
Write the expression to obtain the induced emf between the ends of the conductor.
Here,
Substitute
Substitute
Here,
For maximum induced emf between the ends of the conductor,
Substitute
Conclusion:
Substitute
Therefore, the maximum emf induced between the ends of the conductor is
(b)
The value of the average induced emf for each complete rotation.
(b)

Answer to Problem 46P
The value of the average induced emf for each complete rotation is
Explanation of Solution
Write the expression to obtain the average induced emf for each complete rotation.
Here,
Conclusion:
Substitute
Therefore, the value of the average induced emf for each complete rotation is
(c)
The variation in answers in part (a) and (b) when change in magnetic field is allowed to extent a distance
(c)

Answer to Problem 46P
The answer in part (a) and (b) would be doubled when change in magnetic field is allowed to extent a distance
Explanation of Solution
Consider equation (I).
Substitute
Conclusion:
Substitute
Thus, the maximum emf induced between the ends of the conductor is
Substitute
Thus, the value of the average induced emf for each complete rotation is
Therefore, the answer in part (a) and (b) would be doubled when change in magnetic field is allowed to extent a distance
(d)
The graph between emf versus time when the magnetic field is drawn as shown in the figure P31.46.
(d)

Answer to Problem 46P
The graph between emf versus time is as shown below.
Explanation of Solution
When change in magnetic field is not allowed to extent a distance
Thus, the emf is only in the coil for the half rotation and for the other half rotation, there is no induced emf in the coil.
The graph between emf versus time is as shown below.
Figure-(1)
(d)
The graph between emf versus time when the magnetic field is extended as described in part (c).
(d)

Answer to Problem 46P
The graph between emf versus time is as shown in the figure below.
Explanation of Solution
When the change in magnetic field is allowed to extent a distance
Thus, the emf is induced in the coil in the whole rotation of the coil.
The graph for this case is as shown in the figure below.
Figure-(2)
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Chapter 31 Solutions
Physics for Scientists and Engineers with Modern, Revised Hybrid (with Enhanced WebAssign Printed Access Card for Physics, Multi-Term Courses)
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