The relative orientation of the loops so that their mutual inductance is maximum.

Question

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Answer 1

Question

Chapter 32, Problem 1OQ

(i)

To determine

The relative orientation of the loops so that their mutual inductance is maximum.

(i)

Expert Solution

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)

To determine

The relative orientation of the loops so that their mutual inductance is minimum.

(ii)

Expert Solution

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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Answer 2

Question

Chapter 32, Problem 1OQ

(i)

To determine

The relative orientation of the loops so that their mutual inductance is maximum.

(i)

Expert Solution

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)

To determine

The relative orientation of the loops so that their mutual inductance is minimum.

(ii)

Expert Solution

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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Answer 3

Question

Chapter 32, Problem 1OQ

(i)

To determine

The relative orientation of the loops so that their mutual inductance is maximum.

(i)

Expert Solution

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)

To determine

The relative orientation of the loops so that their mutual inductance is minimum.

(ii)

Expert Solution

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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Answer 4

Question

Chapter 32, Problem 1OQ

(i)

To determine

The relative orientation of the loops so that their mutual inductance is maximum.

(i)

Expert Solution

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)

To determine

The relative orientation of the loops so that their mutual inductance is minimum.

(ii)

Expert Solution

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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Answer 5

Chapter 32, Problem 1OQ

(i)

To determine

The relative orientation of the loops so that their mutual inductance is maximum.

(i)

Expert Solution

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)

To determine

The relative orientation of the loops so that their mutual inductance is minimum.

(ii)

Expert Solution

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.

Answer 6

Chapter 32, Problem 1OQ

(i)

To determine

The relative orientation of the loops so that their mutual inductance is maximum.

(i)

Expert Solution

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.

Answer 7

Chapter 32, Problem 1OQ

(i)

To determine

The relative orientation of the loops so that their mutual inductance is maximum.

Answer 8

(i)

Expert Solution

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.

Answer 9

(i)

Expert Solution

Answer 10

(i)

Expert Solution

Answer 11

Expert Solution

Answer 12

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.

Answer 13

(ii)

To determine

The relative orientation of the loops so that their mutual inductance is minimum.

(ii)

Expert Solution

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.

Answer 14

(ii)

To determine

The relative orientation of the loops so that their mutual inductance is minimum.

Answer 15

(ii)

Expert Solution

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.

Answer 16

(ii)

Expert Solution

Answer 17

(ii)

Expert Solution

Answer 18

Expert Solution

Answer 19

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.

Answer 20

Ch. 32.1 - A coil with zero resistance has its ends labeled a...Ch. 32.2 - Prob. 32.2QQ Ch. 32.3 - Prob. 32.3QQ Ch. 32.4 - Prob. 32.4QQ Ch. 32.5 - (i) At an instant of time during the oscillations...Ch. 32 - Prob. 1OQ Ch. 32 - Prob. 2OQ Ch. 32 - Prob. 3OQ Ch. 32 - Prob. 4OQ Ch. 32 - Prob. 5OQ

The relative orientation of the loops so that their mutual inductance is maximum.

Concept explainers

The relative orientation of the loops so that their mutual inductance is maximum.

Answer to Problem 1OQ

Explanation of Solution

The relative orientation of the loops so that their mutual inductance is minimum.

Answer to Problem 1OQ

Explanation of Solution

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Chapter 32 Solutions