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.
Want to see more full solutions like this?
Chapter 32 Solutions
Physics for Scientists and Engineers with Modern Physics, Technology Update
- Suppose that a rectangular toroid has 2000 windings and a self-inductance of 0.040 H. If h = 0.10 m, what is the current flowing through a rectangular toroid when the energy in its magnetic field is 2.0 × 10-6 J?arrow_forwardA solenoid of N1turns has length l1and radius R1, and a second smaller solenoid of N2turns has length l2and radius R2. The smaller solenoid is placed completely inside the larger solenoid so that their long axes coincide. What is the mutual inductance of the two solenoids?arrow_forwardShow that for the circuit shown below, the initial energy stored in the inductor, LI2(0)/2 , is equal to the total energy eventually dissipated in the resistor 0I2(t)Rdt.arrow_forward
- A 24-V battery is connected in series with a resistor and an inductor, with R = 8.0 V and L = 4.0 H, respectively. Find the energy stored in the inductor (a) when the current reaches its maximum value and (b) one time constant after the switch is closed.arrow_forwardTwo single-turn circular loops of wire have radii R and r, with R >> r. The loops lie in the same plane and are concentric. (a) Show that the mutual inductance of the pair is approximately M = μ0πr2/2R. (b) Evaluate M for r = 2.00 cm and R = 20.0 cm.arrow_forwardTwo identical long wires of radius a =1.53 mm are parallel and carry identical currents in opposite directions.Their center-to-center separation is d = 14.2 cm. Neglect the flux within the wires but consider the flux in the region between the wires.What is the inductance per unit length of the wires?arrow_forward
- Please show how much current is on the battery and on each resistor and the inductor at T is equal to zero and T is equal to infinityarrow_forwardIn a practical electrical circuit, inductors are often coils of wire in the form of a solenoid. Consider a solenoid of length 2.0 cm consisting of 1000 turns of wire. Each turn is a circular loop with a radius of 0.50 cm. Calculate the value of L.arrow_forwardTwo concentric circular coils, one of small radius r1 and the other of large radius r2 , such that r1 << r2 are placed co-axially with centres coinciding. Obtain the mutual inductance of the arrangementarrow_forward
- The self-inductance of a solenoid increases under which of the following conditions?arrow_forwardA 24-V battery is connected in series with a resistor and aninductor, with R = 8.0 Ω and L = 4.0 H, respectively. Find theenergy stored in the inductor (a) when the current reaches itsmaximum value and (b) one time constant after the switch isclosed.arrow_forwardWhen the current through a large inductor is interrupted with a switch, an arc appears across the open terminals of the switch. Explain.arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningGlencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-Hill