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29 March, 05:41

The current in a solenoid is 1.2 A. How many turns must be wound on a 0.25 m solenoid in order to produce a magnetic field of 1 mT within it?

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  1. 29 March, 05:52
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    N = 166 turns

    Explanation:

    Conceptual Analysis

    The magnetic field inside a solenoid is calculated by means of the following formula:

    B = μ₀ * (N/L) * I Formula (1)

    Where:

    B : magnetic field inside the sollenoid (T)

    μ₀ : free space permeability (T*m/A)

    N : number of turns of the solenoid

    L : solenoid length (m)

    I : electric current in the solenoid (A)

    Known data

    I = 1.2 A

    L = 0.25 m

    B = 1 mT = 1 * 10⁻³T

    μ₀ = 4π*10⁻⁷ T*m/A

    Problem development

    We replace data in formula (1) to calculate the number of turns of the solenoid (N):

    B = μ₀ * (N/L) * I

    1 * 10⁻³ = 4π*10⁻⁷ * (N/0.25) * 1.2

    1 * 10⁻³*0.25 = 4π*10⁻⁷*1.2*N

    N = (0.25*10⁻³) / (4π*10⁻⁷*1.2)

    N = 165.78

    N = 166 turns
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