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Ch 27: Magnetic Field and Magnetic Forces
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Young & Freedman Calc 15th EditionCh 27: Magnetic Field and Magnetic Forces문제 9b
27장, 문제 9b

A circular area with a radius of 6.50 cm lies in the xy-plane. What is the magnitude of the magnetic flux through this circle due to a uniform magnetic field B = 0.230 T at an angle of 53.1° from the +z-direction?

검증된 단계별 안내
1
First, understand that magnetic flux (Φ) through a surface is given by the formula: Φ = B * A * cos(θ), where B is the magnetic field, A is the area of the surface, and θ is the angle between the magnetic field and the normal to the surface.
Calculate the area (A) of the circular region. The formula for the area of a circle is A = π * r^2, where r is the radius. Convert the radius from centimeters to meters by dividing by 100, since 1 cm = 0.01 m.
Substitute the given radius (6.50 cm) into the area formula to find A in square meters.
Identify the angle θ. The problem states that the magnetic field is at an angle of 53.1° from the +z-direction. Since the circle lies in the xy-plane, the normal to the surface is along the z-axis. Therefore, θ is the angle between the magnetic field and the normal, which is 53.1°.
Substitute the values of B (0.230 T), A (calculated area), and θ (53.1°) into the magnetic flux formula Φ = B * A * cos(θ) to find the magnitude of the magnetic flux through the circle.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
3m

주요 개념

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

Magnetic Flux

Magnetic flux quantifies the amount of 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. This concept is crucial for understanding how magnetic fields interact with surfaces.
추천 영상:
가이드 코스
04:52
Magnetic Flux

Dot Product

The dot product is a mathematical operation that multiplies two vectors and returns a scalar. It is used to calculate the component of one vector along the direction of another. In the context of magnetic flux, it helps determine the effective magnetic field passing through a surface by considering the angle between the field and the surface normal.
추천 영상:
가이드 코스
09:07
Introduction to Dot Product (Scalar Product)

Trigonometry in Physics

Trigonometry is essential in physics for resolving vector components and calculating angles. In this problem, the cosine function is used to find the component of the magnetic field perpendicular to the circular area. Understanding trigonometric relationships allows for accurate calculations of physical quantities like magnetic flux.
추천 영상:
가이드 코스
3:26
Trigonometry
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