Ch. 27 - Magnetism

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179당신이 사용하는 게 아니라요?교과서 변경

Giancoli Douglas 5th edition

Ch. 27 - Magnetism

문제 7

26장, 문제 7

The magnetic force per meter on a wire is measured to be only 55% of its maximum possible value. What is the angle between the wire and the magnetic field?

검증된 단계별 안내

The magnetic force on a current-carrying wire in a magnetic field is given by the formula:

F = I L B sin θ

, where

F

is the magnetic force,

I

is the current,

L

is the length of the wire,

B

is the magnetic field strength, and

θ

is the angle between the wire and the magnetic field.

The maximum possible magnetic force occurs when

sin θ = 1

, which corresponds to

θ = 90 °

. In this case, the force is

F = I L B

In the problem, the magnetic force is only 55% of its maximum value. This means

sin θ = 0.55

To find the angle

θ

, take the inverse sine (arcsin) of 0.55:

θ = arcsin (0.55)

Use a calculator or mathematical tool to compute the value of

θ

in degrees or radians, depending on the context of the problem.

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.

Magnetic Force on a Current-Carrying Wire

The magnetic force experienced by a wire carrying an electric current in a magnetic field is given by the formula F = I * L * B * sin(θ), where F is the force, I is the current, L is the length of the wire, B is the magnetic field strength, and θ is the angle between the wire and the magnetic field. This relationship shows that the force is maximized when the wire is perpendicular to the magnetic field (θ = 90°) and is zero when parallel (θ = 0°).

Maximum Magnetic Force

The maximum magnetic force occurs when the angle θ is 90 degrees, resulting in sin(θ) being equal to 1. In this scenario, the force is at its peak value, which can be calculated using the formula F_max = I * L * B. Understanding this concept is crucial for determining the actual angle when the force is less than the maximum possible value.

Trigonometric Relationships

Trigonometric functions, particularly the sine function, play a vital role in relating angles to ratios in right triangles. In the context of magnetic forces, the sine of the angle θ determines the proportion of the maximum force that is realized. If the magnetic force is 55% of its maximum, this can be expressed mathematically as sin(θ) = 0.55, allowing for the calculation of the angle using the inverse sine function.