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Ch. 27 - Magnetism
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Non è quello che usi tu?Cambia libro di testo
Capitolo 26, Problema 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?

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The magnetic force on a current-carrying wire in a magnetic field is given by the formula: F=ILBsinθ, 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 sinθ=1, which corresponds to θ=90°. In this case, the force is F=ILB.
In the problem, the magnetic force is only 55% of its maximum value. This means sinθ=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.

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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°).
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Magnetic Force on Current-Carrying Wire

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.
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Magnetic Force on Current-Carrying Wire

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.
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