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).

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
icon
Related questions
Question

Can you help me with part E?

Learning Goal:
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=μencl
(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 №₂ 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)-di-
-Þм(t).
=-
dt
Figure
Radius p
Blue coil N₂ turns
Black coil: n turns
per unit length
1 of 1
Transcribed Image Text:Learning Goal: 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=μencl (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 №₂ 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)-di- -Þм(t). =- dt Figure Radius p Blue coil N₂ turns Black coil: n turns per unit length 1 of 1
Part D
This 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)
Submit
Part E
Previous Answers
Correct
Mutual 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 into
Kirchhoff'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 reflects
Lenz'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 oppose
the 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 ΑΣΦ
Submit
Request Answer
Provide Feedback
?
Next >
Transcribed Image Text:Part D This 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) Submit Part E Previous Answers Correct Mutual 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 into Kirchhoff'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 reflects Lenz'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 oppose the 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 ΑΣΦ Submit Request Answer Provide Feedback ? Next >
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Knowledge Booster
Ferromagnetism
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON