Concept explainers
(i)
The relative orientation of the loops so that their mutual inductance is maximum.
(i)
Answer to Problem 1OQ
The loops are oriented parallel to each other so that mutual induction is maximum. Thus, option (a) coaxial and lying in parallel planes is correct.
Explanation of Solution
The two circular loops are separated by a fixed distance, thus, for the maximum mutual inductance; the two loops should be coaxial and lying in parallel planes. This is because of the reason that if these loops are arranged parallel to each other, then the flux through one loop is entirely passing through the other loop. Hence, the mutual inductance is maximum when the loops are parallel to each other.
Conclusion:
Since, the mutual inductance is maximum when the loops are oriented parallel to each other, therefore, option (a) is correct.
When the loops are lying in the same plane, there is no flux linkage between the two loops. Therefore, option (b) is incorrect.
When the loops are lying in the perpendicular planes, with the center of one on the axis of the other, the mutual inductance is minimum. Therefore, option (c) is incorrect.
Since, the mutual inductance depends on the orientation of the loops, therefore, option (d) is incorrect.
(ii)
The relative orientation of the loops so that their mutual inductance is minimum.
(ii)
Answer to Problem 1OQ
The loops are oriented perpendicular to each other so that mutual induction is minimum. Thus, option (c) lying in the perpendicular planes, with the center of one on the axis of the other; is correct.
Explanation of Solution
The two circular loops are separated by a fixed distance, thus, for the minimum mutual inductance; the two loops should be lying in the perpendicular planes, with the center of one on the axis of the other. This is because of the reason that if these loops are arranged perpendicular to each other, then the flux through one loop does not pass through the other loop. Hence, the mutual inductance is minimum when the loops are perpendicular to each other.
Conclusion:
Since, the mutual inductance is minimum when the loops are oriented perpendicular to each other, therefore, option (c) is correct.
When the loops are coaxial and lying in the parallel planes, the mutual inductance is maximum. Therefore, option (a) is incorrect.
When the loops are lying in the same plane, there is no flux linkage between the two loops. Therefore, option (b) is incorrect.
Since, the mutual inductance depends on the orientation of the loops, therefore, option (d) is incorrect.
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Chapter 32 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
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