Ch 29: Electromagnetic Induction

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610당신이 사용하는 게 아니라요?교과서 변경

Young & Freedman Calc 14th Edition

Ch 29: Electromagnetic Induction

문제 1b

29장, 문제 1b

A single loop of wire with an area of 0.0900 m² is in a uniform magnetic field that has an initial value of 3.80 T, is perpendicular to the plane of the loop, and is decreasing at a constant rate of 0.190 T/s. If the loop has a resistance of 0.600 Ω, find the current induced in the loop.

검증된 단계별 안내

Start by understanding 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. The formula is:

ε = - \frac{Φ>}{t>}

Calculate the change in magnetic flux,

Φ

, using the formula:

Φ = B A

, where

B

is the magnetic field and

A

is the area of the loop. Since the magnetic field is decreasing, the rate of change of the magnetic field is given as

-0.190 T/s

Substitute the values into the formula for EMF:

ε = - A \frac{B>}{t>}

. Here,

A = 0.0900 m

² and

\frac{B>}{t>} = -0.190 T/s

Use Ohm's Law to find the induced current,

I

, in the loop. Ohm's Law states that

I = \frac{ε}{R}

, where

R

is the resistance of the loop, given as

0.600 Ω

Substitute the calculated EMF into Ohm's Law to find the current:

I = \frac{ε}{0.600}

. This will give you the magnitude of the induced current in the loop.

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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 loop induces an electromotive force (EMF) in the wire. The induced EMF is proportional to the rate of change of the magnetic flux. In this scenario, the decreasing magnetic field causes a change in flux, leading to an induced EMF in the loop.

Magnetic Flux

Magnetic flux is the product of the magnetic field strength and the area it penetrates, perpendicular to the field lines. It quantifies the total magnetic field passing through a surface. Here, the flux changes due to the decreasing magnetic field, which is crucial for calculating the induced EMF using Faraday's Law.

Ohm's Law

Ohm's Law relates the current flowing through a conductor to the voltage across it and its resistance, expressed as I = V/R. In this problem, the induced EMF acts as the voltage, and the loop's resistance is given, allowing us to calculate the induced current using this fundamental principle.