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Ch 30: Inductance
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoYoung & Freedman Calc 14th EditionCh 30: InductanceProblema 13a
Capitolo 30, Problema 13a

A toroidal solenoid has mean radius 12.0 cm and crosssectional area 0.600 cm2. How many turns does the solenoid have if its inductance is 0.100 mH?

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Start by recalling the formula for the inductance of a toroidal solenoid: \( L = \frac{\mu_0 N^2 A}{2\pi r} \), where \( L \) is the inductance, \( \mu_0 \) is the permeability of free space \( (4\pi \times 10^{-7} \text{ Tm/A}) \), \( N \) is the number of turns, \( A \) is the cross-sectional area, and \( r \) is the mean radius.
Convert the given measurements to meters: the mean radius \( r = 12.0 \text{ cm} = 0.12 \text{ m} \) and the cross-sectional area \( A = 0.600 \text{ cm}^2 = 0.0000600 \text{ m}^2 \).
Rearrange the formula to solve for the number of turns \( N \): \( N = \sqrt{\frac{2\pi r L}{\mu_0 A}} \).
Substitute the known values into the rearranged formula: \( L = 0.100 \text{ mH} = 0.0001 \text{ H} \), \( r = 0.12 \text{ m} \), \( A = 0.0000600 \text{ m}^2 \), and \( \mu_0 = 4\pi \times 10^{-7} \text{ Tm/A} \).
Calculate the number of turns \( N \) using the substituted values in the formula: \( N = \sqrt{\frac{2\pi \times 0.12 \times 0.0001}{4\pi \times 10^{-7} \times 0.0000600}} \).

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Inductance

Inductance is a property of an electrical conductor that quantifies its ability to induce an electromotive force (EMF) when the current flowing through it changes. It is measured in henries (H) and is a crucial factor in the design of coils and solenoids, as it determines how effectively they can store magnetic energy.
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Mutual Induction

Toroidal Solenoid

A toroidal solenoid is a coil of wire shaped like a doughnut, with the wire wound around a circular core. This configuration confines the magnetic field within the core, minimizing external magnetic interference. The inductance of a toroidal solenoid depends on its number of turns, cross-sectional area, and the core's permeability.
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Toroidal Solenoids aka Toroids

Magnetic Permeability

Magnetic permeability is a measure of how easily a material can support the formation of a magnetic field within itself. It is a key factor in determining the inductance of a solenoid, as materials with higher permeability allow for stronger magnetic fields, thus increasing the solenoid's inductance. The permeability of free space (vacuum) is a constant used in calculations involving inductance.
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Magnetic Fields and Magnetic Dipoles
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