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Ch 29: Electromagnetic Induction
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552당신이 사용하는 게 아니라요?교과서 변경
29장, 문제 37

A long, straight solenoid with a cross-sectional area of 8.00 cm2 is wound with 90 turns of wire per centimeter, and the windings carry a current of 0.350 A. A second winding of 12 turns encircles the solenoid at its center. The current in the solenoid is turned off such that the magnetic field of the solenoid becomes zero in 0.0400 s. What is the average induced emf in the second winding?

검증된 단계별 안내
1
First, understand that the solenoid creates a magnetic field when current flows through it. The magnetic field inside a long solenoid is given by the formula: B=μnI, where μ is the permeability of free space, n is the number of turns per unit length, and I is the current.
Calculate the initial magnetic field inside the solenoid using the given values: n=90/1cm (convert to meters), I=0.350A, and μ=4π×107Tm/A.
Determine the change in magnetic flux through the second winding. The magnetic flux Φ is given by Φ=BA, where A is the cross-sectional area of the solenoid. Initially, Φ is non-zero, and finally, it becomes zero when the current is turned off.
Use Faraday's law of electromagnetic induction to find the average induced emf in the second winding. Faraday's law states that the induced emf ε is equal to the negative rate of change of magnetic flux: ε=-ΔΦΔt. Calculate ΔΦ and divide by the time interval Δt=0.0400s.
Finally, multiply the induced emf by the number of turns in the second winding to find the total average induced emf. The second winding has 12 turns, so the total induced emf is ε×12.

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주요 개념

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

Faraday's Law of Electromagnetic Induction

Faraday's Law states that a change in magnetic flux through a circuit induces an electromotive force (emf) in the circuit. The induced emf is proportional to the rate of change of the magnetic flux. In this problem, the solenoid's magnetic field changes, inducing an emf in the second winding.
추천 영상:

Magnetic Flux

Magnetic flux is the product of the magnetic field and the area it penetrates, perpendicular to the field lines. It is a measure of the quantity of magnetism, considering the strength and extent of a magnetic field. The change in magnetic flux through the second winding is crucial for calculating the induced emf.
추천 영상:

Solenoid Magnetic Field

A solenoid generates a uniform magnetic field inside its coils when a current passes through it. The field strength is determined by the number of turns per unit length and the current. Understanding how the solenoid's field changes when the current is turned off helps in determining the change in magnetic flux and the resulting induced emf.
추천 영상:
가이드 코스
13:54
Magnetic Field Produced by Loops and Solenoids
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