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(7) - dỉ = µ-encl (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() dl=м(t).

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Chapter1: Units, Trigonometry. And Vectors
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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 C
Now find the electromotive force ε (t) induced across the entirety of solenoid 2 by the change in current in solenoid 1.
Express your answer in terms of dI, (t)/dt, n₁, N₂, other parameters given in the introduction, and any relevant constants.
▸ View Available Hint(s)
E2(t) =
Ο ΑΣΦ
Submit Previous Answers
* Incorrect; Try Again
Transcribed Image Text:Part C Now find the electromotive force ε (t) induced across the entirety of solenoid 2 by the change in current in solenoid 1. Express your answer in terms of dI, (t)/dt, n₁, N₂, other parameters given in the introduction, and any relevant constants. ▸ View Available Hint(s) E2(t) = Ο ΑΣΦ Submit Previous Answers * Incorrect; Try Again
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