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).
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Can you help me with part E?
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
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)
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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
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