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An induction furnace uses
(a)
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Answer to Problem 31.80CP
Explanation of Solution
Given info: Radius of disk is
Since the eddy currents occur as concentric circles with the disk. Consider the disk to be a collection of rings that each has an induced emf.
The emf induced in the disk can be given as,
Here,
Substitute
Here,
The elemental resistance around the ring can be given as,
Here,
Substitute
The power delivered to the elemental ring can be given as,
Substitute
The total power delivered to the disk can be given as,
Substitute
Substitute
Here,
Thus, the average power delivered to the disk can be given as
Conclusion:
Therefore, the average power delivered to the disk can be given as
(b)
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Answer to Problem 31.80CP
Answer The factor by which power will change when the field doubles is four times.
Explanation of Solution
Given info: Radius of disk is
Explanation:
The relation between the field and the power can be given from equation (1) as,
Substitute
Thus, the power will change by four times when the field doubles.
Conclusion:
Therefore, the factor by which power will change when the field doubles is four times.
(c)
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Answer to Problem 31.80CP
Answer The factor by which power will change when the frequency doubles is four times.
Explanation of Solution
Given info: Radius of disk is
Explanation:
The relation between the field and the power can be given from equation (1) as,
Substitute
Here,
Substitute
Thus, the power will change by four times when the frequency doubles.
Conclusion:
Therefore, the factor by which power will change when the frequency doubles is four times.
(d)
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Answer to Problem 31.80CP
Answer The factor by which power will change when the radius of the disk doubles is sixteen times.
Explanation of Solution
Given info: Radius of disk is
Explanation:
The relation between the field and the power can be given from equation (1) as,
Substitute
Thus, the power will change by sixteen times when the radius of disk doubles.
Conclusion:
Therefore, the factor by which power will change when the radius of disk doubles is sixteen times.
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Chapter 31 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
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