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Ch 28: Sources of Magnetic Field
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoYoung & Freedman Calc 14th EditionCh 28: Sources of Magnetic FieldProblema 46
Capitolo 28, Problema 46

A 15.0 cm long solenoid with radius 0.750 cm is closely wound with 600 turns of wire. The current in the windings is 8.00 A. Compute the magnetic field at a point near the center of the solenoid.

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Understand the formula for the magnetic field inside a solenoid: The magnetic field inside a solenoid is given by the formula: B=μnI, where B is the magnetic field, μ is the permeability of free space (μ=4π×10⁻7Tm/A), n is the number of turns per unit length, and I is the current.
Calculate the number of turns per unit length: The solenoid has 600 turns and a length of 15.0 cm. Convert the length to meters: 15.0/100=0.15 meters. Then, calculate n as n=600/0.15 turns per meter.
Substitute the values into the formula: Use the values μ=4π×10⁻7, n from the previous step, and I=8.00 A into the formula B=μnI.
Perform the multiplication: Multiply the values of μ, n, and I to find the magnetic field B.
Interpret the result: The calculated magnetic field B represents the strength of the magnetic field at a point near the center of the solenoid, which is uniform and parallel to the axis of the solenoid.

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Magnetic Field of a Solenoid

The magnetic field inside a long solenoid is uniform and parallel to the axis of the solenoid. It is given by the formula B = μ₀ * n * I, where B is the magnetic field, μ₀ is the permeability of free space, n is the number of turns per unit length, and I is the current. This formula assumes the solenoid is infinitely long, but it provides a good approximation near the center of a finite solenoid.
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Permeability of Free Space

The permeability of free space, denoted as μ₀, is a fundamental physical constant that describes the ability of a vacuum to support the formation of a magnetic field. Its value is approximately 4π × 10⁻⁷ T·m/A. This constant is crucial in calculating the magnetic field in various electromagnetic contexts, including solenoids.
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Turns per Unit Length

Turns per unit length, denoted as n, is a measure of how many loops of wire are wound per unit length of the solenoid. It is calculated by dividing the total number of turns by the length of the solenoid. This parameter is essential in determining the strength of the magnetic field inside the solenoid, as it directly influences the field's magnitude according to the formula B = μ₀ * n * I.
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