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

Question

Want to see more full solutions like this?

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.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Students have asked these similar questions

Question B3 Consider the following FLRW spacetime: t2 ds² = -dt² + (dx² + dy²+ dz²), t2 where t is a constant. a) State whether this universe is spatially open, closed or flat. [2 marks] b) Determine the Hubble factor H(t), and represent it in a (roughly drawn) plot as a function of time t, starting at t = 0. [3 marks] c) Taking galaxy A to be located at (x, y, z) = (0,0,0), determine the proper distance to galaxy B located at (x, y, z) = (L, 0, 0). Determine the recessional velocity of galaxy B with respect to galaxy A. d) The Friedmann equations are 2 k 8πG а 4πG + a² (p+3p). 3 a 3 [5 marks] Use these equations to determine the energy density p(t) and the pressure p(t) for the FLRW spacetime specified at the top of the page. [5 marks] e) Given the result of question B3.d, state whether the FLRW universe in question is (i) radiation-dominated, (ii) matter-dominated, (iii) cosmological-constant-dominated, or (iv) none of the previous. Justify your answer. f) [5 marks] A conformally…

SECTION B Answer ONLY TWO questions in Section B [Expect to use one single-sided A4 page for each Section-B sub question.] Question B1 Consider the line element where w is a constant. ds²=-dt²+e2wt dx², a) Determine the components of the metric and of the inverse metric. [2 marks] b) Determine the Christoffel symbols. [See the Appendix of this document.] [10 marks] c) Write down the geodesic equations. [5 marks] d) Show that e2wt it is a constant of geodesic motion. [4 marks] e) Solve the geodesic equations for null geodesics. [4 marks]

Page 2 SECTION A Answer ALL questions in Section A [Expect to use one single-sided A4 page for each Section-A sub question.] Question A1 SPA6308 (2024) Consider Minkowski spacetime in Cartesian coordinates th = (t, x, y, z), such that ds² = dt² + dx² + dy² + dz². (a) Consider the vector with components V" = (1,-1,0,0). Determine V and V. V. (b) Consider now the coordinate system x' (u, v, y, z) such that u =t-x, v=t+x. [2 marks] Write down the line element, the metric, the Christoffel symbols and the Riemann curvature tensor in the new coordinates. [See the Appendix of this document.] [5 marks] (c) Determine V", that is, write the object in question A1.a in the coordinate system x'. Verify explicitly that V. V is invariant under the coordinate transformation. Question A2 [5 marks] Suppose that A, is a covector field, and consider the object Fv=AAμ. (a) Show explicitly that F is a tensor, that is, show that it transforms appropriately under a coordinate transformation. [5 marks] (b)…

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.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

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.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

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.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

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

Want to see more full solutions like this?

Chapter 32 Solutions