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 1a

29장, 문제 1a

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. What emf is induced in this loop?

검증된 단계별 안내

Start by recalling Faraday's Law of Induction, which states that the induced electromotive force (emf) in a loop is equal to the negative rate of change of magnetic flux through the loop. The formula is:

ε = - d Φ d t

, where

Φ

is the magnetic flux.

Calculate the initial magnetic flux through the loop using the formula:

Φ = B A

, where

B

is the magnetic field strength and

A

is the area of the loop. Substitute the given values:

Φ = 3.80 T × 0.0900 m

².

Determine the rate of change of the magnetic flux. Since the magnetic field is decreasing at a constant rate, the change in magnetic flux can be expressed as:

d Φ d t = A d B d t

. Substitute the area and the rate of change of the magnetic field:

d Φ d t = 0.0900 m

² × (-0.190 T/s).

Apply Faraday's Law to find the induced emf. Substitute the rate of change of magnetic flux into the formula:

ε = - d Φ d t

. This will give you the magnitude of the induced emf.

Remember that the negative sign in Faraday's Law indicates the direction of the induced emf according to Lenz's Law, which states that the induced emf will generate a current that opposes the change in magnetic flux. However, for the magnitude, you can consider the absolute value.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

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 loop. The induced emf is equal to the negative rate of change of magnetic flux through the loop. This principle is crucial for understanding how varying magnetic fields can generate electric currents.

Magnetic Flux

Magnetic flux refers to the total magnetic field passing through a given area, such as a loop of wire. 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. In this problem, the magnetic field is perpendicular to the loop, simplifying the calculation of flux.

Rate of Change of Magnetic Field

The rate of change of the magnetic field is a key factor in determining the induced emf. In this scenario, the magnetic field is decreasing at a constant rate, which directly affects the rate of change of magnetic flux. Understanding this rate is essential for applying Faraday's Law to calculate the induced emf in the loop.