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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 47a
Capitolo 28, Problema 47a

A solenoid is designed to produce a magnetic field of 0.0270 T at its center. It has radius 1.40 cm and length 40.0 cm, and the wire can carry a maximum current of 12.0 A. What minimum number of turns per unit length must the solenoid have?

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Start by recalling the formula for the magnetic field inside a solenoid: B = μ0nI, 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.
Identify the given values: B = 0.0270 T, I = 12.0 A, and μ0 = 4π × 10-7 T·m/A.
Rearrange the formula to solve for n: n = B / (μ0I).
Substitute the known values into the rearranged formula: n = 0.0270 / (4π × 10-7 × 12.0).
Calculate the expression to find the minimum number of turns per unit length required for the solenoid to produce the desired magnetic field.

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Magnetic Field in a Solenoid

The magnetic field inside a solenoid is uniform and parallel to the axis of the solenoid. It is given by the formula B = μ₀nI, 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. Understanding this relationship is crucial for calculating the required number of turns per unit length to achieve a specific magnetic field.
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Permeability of Free Space

Permeability of free space, denoted as μ₀, is a fundamental physical constant that describes the ability of a vacuum to support a magnetic field. Its value is approximately 4π × 10⁻⁷ T·m/A. This constant is essential in calculating the magnetic field produced by a solenoid, as it directly influences the strength of the field for a given current and number of turns.
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Turns per Unit Length

Turns per unit length, represented by n, is a measure of how many loops of wire are present per unit length of the solenoid. It is a critical factor in determining the magnetic field strength inside the solenoid. To find the minimum number of turns per unit length required to produce a specific magnetic field, one must rearrange the solenoid magnetic field formula to solve for n, considering the given current and desired field strength.
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