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Ch 29: Electromagnetic Induction
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Young & Freedman Calc 14th EditionCh 29: Electromagnetic Induction문제 37d
29장, 문제 37d

The magnetic field within a long, straight solenoid with a circular cross section and radius R is increasing at a rate of dB/dt. What is the magnitude of the induced emf in a circular turn of radius R/2 that has its center on the solenoid axis?

검증된 단계별 안내
1
Understand that the problem involves electromagnetic induction, specifically Faraday's law of induction, which states that the induced electromotive force (emf) in a closed loop is equal to the negative rate of change of magnetic flux through the loop.
Identify the relevant parameters: the solenoid has a circular cross-section with radius R, and the rate of change of the magnetic field is given as dB/dt. The circular turn has a radius of R/2 and is centered on the solenoid axis.
Calculate the area of the circular turn using the formula for the area of a circle: A = π(R/2)^2. This area will be used to determine the magnetic flux through the turn.
Express the magnetic flux Φ through the circular turn as Φ = B * A, where B is the magnetic field and A is the area of the turn. Since the magnetic field is changing, the flux will also change over time.
Apply Faraday's law to find the magnitude of the induced emf: emf = |dΦ/dt| = |A * dB/dt|. Substitute the area calculated in step 3 and the given rate of change of the magnetic field to find the magnitude of the induced emf.

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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 context, the changing magnetic field inside the solenoid induces an emf in the circular turn.
추천 영상:
가이드 코스
09:26
Faraday's Law

Magnetic Flux

Magnetic flux is the measure of the magnetic field passing through a given area. It is calculated as the product of the magnetic field strength, the area it penetrates, and the cosine of the angle between the field and the normal to the surface. For a circular turn within a solenoid, the flux depends on the solenoid's magnetic field and the area of the turn.
추천 영상:
가이드 코스
04:52
Magnetic Flux

Induced Emf in a Solenoid

The induced emf in a loop within a solenoid is determined by the rate of change of magnetic flux through the loop. For a solenoid, the magnetic field is uniform inside and zero outside, and the emf in a loop of radius R/2 is calculated using the area of the loop and the rate of change of the magnetic field inside the solenoid.
추천 영상:
가이드 코스
09:57
Motional EMF
관련 실천
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