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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 12
27장, 문제 12

A horizontal rectangular surface has dimensions 2.80 cm by 3.20 cm and is in a uniform magnetic field that is directed at an angle of 30.0° above the horizontal. What must the magnitude of the magnetic field be to produce a flux of 3.10 x 10-4 Wb through the surface?

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 strength, A is the area of the surface, and θ is the angle between the magnetic field and the normal (perpendicular) to the surface.
Calculate the area (A) of the rectangular surface. Convert the dimensions from centimeters to meters: 2.80 cm = 0.028 m and 3.20 cm = 0.032 m. Then, multiply these to find the area: A = 0.028 m * 0.032 m.
Identify the angle θ. Since the magnetic field is directed at an angle of 30.0° above the horizontal, the angle between the magnetic field and the normal to the surface is 90° - 30° = 60°.
Rearrange the magnetic flux formula to solve for the magnetic field strength (B): B = Φ / (A * cos(θ)).
Substitute the known values into the equation: Φ = 3.10x10^-4 Wb, A = 0.028 m * 0.032 m, and θ = 60°. Calculate cos(60°) and use these values to find B.

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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. Understanding magnetic flux is crucial for determining how the field interacts with surfaces.
추천 영상:
가이드 코스
04:52
Magnetic Flux

Area Calculation

The area of a surface is essential for calculating magnetic flux. For a rectangle, the area is found by multiplying its length by its width. In this problem, the area of the rectangular surface is 2.80 cm x 3.20 cm, which must be converted to square meters for consistency in units when calculating flux.
추천 영상:
가이드 코스
04:05
Calculating Work As Area Under F-x Graphs

Trigonometric Functions

Trigonometric functions, particularly cosine, are used to resolve the component of the magnetic field perpendicular to the surface. The angle given in the problem (30.0°) is used to find the effective magnetic field component that contributes to the flux, using the formula: flux = B * A * cos(θ), where θ is the angle between the field and the surface normal.
추천 영상:
가이드 코스
08:30
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