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Ch 30: Inductance
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoYoung & Freedman Calc 15th EditionCh 30: InductanceProblema 5a
Capitolo 30, Problema 5a

A 2.50-mH toroidal solenoid has an average radius of 6.00 cm and a cross-sectional area of 2.00 cm2. How many coils does it have? (Make the same assumption as in Example 30.3.)

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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, \( N \) is the number of turns, \( A \) is the cross-sectional area, and \( r \) is the average radius.
Rearrange the formula to solve for the number of turns \( N \): \( N = \sqrt{\frac{2\pi r L}{\mu_0 A}} \).
Substitute the given values into the equation: \( L = 2.50 \times 10^{-3} \text{ H} \), \( r = 6.00 \times 10^{-2} \text{ m} \), and \( A = 2.00 \times 10^{-4} \text{ m}^2 \).
Use the value of the permeability of free space \( \mu_0 = 4\pi \times 10^{-7} \text{ T}\cdot\text{m/A} \) in the equation.
Calculate \( N \) using the rearranged formula and the substituted values to find the number of coils in the toroidal solenoid.

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Inductance of a Solenoid

Inductance is a measure of the ability of a solenoid to store energy in its magnetic field. For a toroidal solenoid, the inductance (L) is determined by the number of turns (N), the cross-sectional area (A), and the average radius (r) of the solenoid. The formula L = (μ₀N²A)/(2πr) relates these parameters, where μ₀ is the permeability of free space.
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Mutual Induction

Toroidal Solenoid

A toroidal solenoid is a coil shaped like a doughnut, with wire wound around a circular path. Unlike a straight solenoid, a toroidal solenoid confines the magnetic field within its core, minimizing external magnetic fields. This design is crucial for applications requiring minimal interference with surrounding components.
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Toroidal Solenoids aka Toroids

Permeability of Free Space

The permeability of free space (μ₀) is a fundamental physical constant that describes how a magnetic field interacts with a vacuum. It is essential in calculating the inductance of solenoids and other electromagnetic devices. Its value is approximately 4π × 10⁻⁷ T·m/A, and it helps determine the strength of the magnetic field generated by a current-carrying coil.
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Spinning Space Station
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