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Ch 30: Inductance
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Young & Freedman Calc 14th EditionCh 30: Inductance문제 7a
30장, 문제 7a

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.)

검증된 단계별 안내
1
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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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.
추천 영상:
가이드 코스
12:59
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.
추천 영상:
가이드 코스
11:47
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.
추천 영상:
가이드 코스
5:05
Spinning Space Station
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