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Ch 30: Electromagnetic Induction
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796당신이 사용하는 게 아니라요?교과서 변경
30장, 문제 49

CALC An electric generator has an 18-cm-diameter, 120-turn coil that rotates at 60 Hz in a uniform magnetic field that is perpendicular to the rotation axis. What magnetic field strength is needed to generate a peak voltage of 170 V?

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Understand the problem: The generator produces an alternating voltage due to the rotation of the coil in a magnetic field. The peak voltage (emf) is given by the formula: Vpeak=NABω, where N is the number of turns, A is the area of the coil, B is the magnetic field strength, and ω is the angular velocity. We need to solve for B.
Calculate the area of the coil: The coil is circular with a diameter of 18 cm. The radius is half the diameter, so r=18/2=9 cm or 0.09 m. The area of the coil is given by A=πr^2=π(0.09)^2.
Determine the angular velocity: The coil rotates at a frequency of 60 Hz. The angular velocity is related to the frequency by the formula ω=2πf, where f is the frequency. Substitute f=60 Hz to find ω.
Rearrange the peak voltage formula to solve for B: Using Vpeak=NABω, isolate B to get B=Vpeak/(NAω). Substitute the known values: Vpeak=170 V, N=120, A (calculated in step 2), and ω (calculated in step 3).
Perform the substitution and simplify the expression to find the magnetic field strength B. Ensure all units are consistent (e.g., meters for area, radians per second for angular velocity) before calculating.

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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 coil induces an electromotive force (EMF) in the coil. The induced voltage is proportional to the rate of change of the magnetic flux and the number of turns in the coil. This principle is fundamental in understanding how generators convert mechanical energy into electrical energy.
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Magnetic Flux

Magnetic flux is defined as the product of the magnetic field strength and the area through which the field lines pass, taking into account the angle between the field lines and the normal to the surface. It is measured in Weber (Wb) and is crucial for calculating the induced voltage in a coil as it directly relates to the amount of magnetic field interacting with the coil.
추천 영상:

Peak Voltage in AC Generators

In alternating current (AC) generators, the peak voltage is the maximum voltage produced during one cycle of rotation. It can be calculated using the formula V_peak = N * A * B * ω, where N is the number of turns, A is the area of the coil, B is the magnetic field strength, and ω is the angular frequency. Understanding this relationship is essential for determining the required magnetic field strength to achieve a specific peak voltage.
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RMS Current and Voltage
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