Can you help me with part E? Learning Goal:To learn about mutual inductance from an example of a long solenoid with twowindings.To illustrate the calculation of mutual inductance it is helpful to consider the specificexample of two solenoids that are wound on a common cylinder. We will take thecylinder to have radius p and length L. Assume that the solenoid is much longer thanits radius, so that its field can be determined from Ampère's law throughout its entirelength: B(+)-di=μencl(Figure 1)We will consider the field that arises from solenoid 1, which has n₁ turns per unitlength. The magnetic field due to solenoid 1 passes (entirely, in this case) throughsolenoid 2, which has №₂ turns (total turns not turns per length). Any change inmagnetic flux from the field generated by solenoid 1 induces an EMF in solenoid 2through Faraday's law of induction. E(F)-di--Þм(t).=-dtFigureRadius pBlue coil N₂ turnsBlack coil: n turnsper unit length1 of 1 Part DThis overall interaction is summarized using the symbol M21 to indicate the mutual inductance between the two windings. Based on your previous two answers, which of the following formulas do you think is the correct one?E2(t) = -M2111(t)E2(t) = -M2111(t)E2(t) = -M211(t)I₁(t) = -M212(t)11(t) = -M21ε2(t)SubmitPart EPrevious AnswersCorrectMutual inductance indicates that a change in the current in solenoid 1 induces an electromotive force (EMF) in solenoid 2. When the double solenoid is thought of as a circuit element, this electromotive force is added intoKirchhoff's loop law. The constant of proportionality is the mutual inductance, denoted by M21. The negative sign in the equation ε2(t) = -M211(t) comes from the negative sign in Faraday's law, and reflectsLenz's rule: The changing magnetic field due to solenoid 1 will induce a current in solenoid 2; this induced current will itself generate a magnetic field within solenoid 2, such that changes in the induced magnetic field opposethe changes in the magnetic field from solenoid 1.Using the formula for the mutual inductance, E2(t) = -M2111(t), find M21.Express the mutual inductance M21 in terms of N1, N2, quantities given in the introduction, and relevant physical constants.M21 =ΜΕ ΑΣΦSubmitRequest AnswerProvide Feedback?Next >

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To learn about mutual inductance from an example of a long solenoid with two windings. To illustrate the calculation of mutual inductance it is helpful to consider the specific example of two solenoids that are wound on a common cylinder. We will take the cylinder to have radius p and length L. Assume that the solenoid is much longer than its radius, so that its field can be determined from Ampère's law throughout its entire length: B(+)-di=40Ienel (Figure 1) We will consider the field that arises from solenoid 1, which has n₁ turns per unit length. The magnetic field due to solenoid 1 passes (entirely, in this case) through solenoid 2, which has N₂ turns (total turns not turns per length). Any change in magnetic flux from the field generated by solenoid 1 induces an EMF in solenoid 2 through Faraday's law of induction. §E(F)-dl = -M(t).

To learn about mutual inductance from an example of a long solenoid with two windings. To illustrate the calculation of mutual inductance it is helpful to consider the specific example of two solenoids that are wound on a common cylinder. We will take the cylinder to have radius p and length L. Assume that the solenoid is much longer than its radius, so that its field can be determined from Ampère's law throughout its entire length: B(+)-di=40Ienel (Figure 1) We will consider the field that arises from solenoid 1, which has n₁ turns per unit length. The magnetic field due to solenoid 1 passes (entirely, in this case) through solenoid 2, which has N₂ turns (total turns not turns per length). Any change in magnetic flux from the field generated by solenoid 1 induces an EMF in solenoid 2 through Faraday's law of induction. §E(F)-dl = -M(t).

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter13: Electromagnetic Induction

Section: Chapter Questions

Problem 13.9CYU: Check Your Understanding A long solenoid of cross-section area 5.0 cm2is wound with 25 turns of wire...

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