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30 September, 21:25

Tia needs to produce a solenoid that has an inductance of 3.01 μ H 3.01 μH. She constructs the solenoid by uniformly winding 1.13 m 1.13 m of thin wire around a tube. How long, in centimeters, should the tube be?

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  1. 30 September, 21:34
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    Answer: 13 cm

    Explanation:

    Given

    Inductance of the solenoid, L = 3.01•10⁻⁶ H

    Width of the wire, x = 1.13 m

    Length of the tube, z = ?

    Now, we know that

    L = μ₀N²A/z, where

    N = x/2πr, making r subject of formula,

    r = x/2πN

    Also,

    A = πr², on substituting for A, we have

    A = πx²/4π²N²

    Now finally, we substitute in the initial equation and solve

    L = μ₀N²A/z

    L = μ₀N²πx²/4π²N²z

    L = μ₀x²/4z, making z subject of formula, we have

    z = μ₀x²/4L

    z = 4π*10⁻⁷ * 1.13² / 4 * 3.01*10⁻⁶

    z = (4π*10⁻⁷ * 1.2769) / (4 * 3.01*10⁻⁶)

    z = 1.6*10^-6 / 1.2*10^-5

    z = 0.13 m

    Therefore, the length of the tube should be 13 cm
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