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One solenoid is centered inside another. The outer one has a length of 50.0 $\mathrm{cm}$ and contains 6750 coils, while the coaxial inner solenoid is 3.0 $\mathrm{cm}$ long and 0.120 $\mathrm{cm}$ in diameter and contains 15 coils. The current in the outer solenoid is changing at 37.5 $\mathrm{A} / \mathrm{s}$ (a) What is the mutual inductance of these solenoids? (b) Find the emf induced in the inner solenoid.

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a. 0.288b. $1.08 \times 10^{-5} \mathrm{V}$

Physics 102 Electricity and Magnetism

Chapter 21

Electromagnetic Induction

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Magnetic Field and Magnetic Forces

Sources of Magnetic field

Inductance

Alternating Current

Rutgers, The State University of New Jersey

Hope College

University of Sheffield

McMaster University

Lectures

03:27

Electromagnetic induction is the production of an electromotive force (emf) across a conductor due to its dynamic interaction with a magnetic field. Michael Faraday is generally credited with the discovery of electromagnetic induction in 1831.

08:42

In physics, a magnetic field is a vector field that describes the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude (or strength); as such it is a vector field. The term is used for two distinct but closely related fields denoted by the symbols B and H, where H is measured in units of amperes per meter (usually in the cgs system of units) and B is measured in teslas (SI units).

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One solenoid is centered i…

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Two solenoids $A$ and $B$ …

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A toroidal solenoid has 50…

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Two solenoids A and B, spa…

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Two solenoids $A$ and $B$,…

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A solenoidal coil with 25 …

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A long, cylindrical soleno…

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03:17

So for a question, 30 for party, the mutual induct insult to Silla noise would be equal to mu, not the magnetic permeability in a vacuum times thie area times the number of turns in one soul annoyed times the number of turns in the second sill in oId divided by l so this would be equal to four pi times 10 to the negative seventh times pi are so pi r squared would be the cross sectional area. This would be a pi times 6.0 times 10 to the negative fourth meters squared times 6,750 times 15 and this will be divided by the distance. So this would be the point 500 meters. And so the mutual induct ins's between these two soul noise is going to be 2.88 times 10 to the negative seventh Henry's and then for part B. They're asking us to find the IMF so we know that you can say that the IMF absalon sub too in Seoul, annoyed too, is produced by changing current. I said one in Seoul, annoyed one. So we can say that Absalon sub two is going to be equal to the mutual induct inst times. The absolute value of the change in current in Seoul annoyed one with respect to time. This is going to be equal to em. What we found originally. So it would be two 0.88 times 10 to the negative seventh Henry's and then it would be multiplied bye, 37.5 amps per second. And we find that the IMF and still annoyed too, is going to be equal to 1.8 times 10 to the negative fifth volts. So this would be your answer for the IMF and soul annoyed too. And this would be our mutual induct, insp. Between the two soul nights, that is the end of the solution. Thank you for watching.

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