Two long parallel wires carry currents of 3.35 A and 6.99 A . The magnitude of the force per unit length acting on each wire is 6.03 × 10 −

Question

Two long parallel wires carry currents of 3.35 A and 6.99 A . The magnitude of the force per unit length acting on each wire is 6.03 × 10 − 5 N / m . Find the separation distance d of the wires expressed in millimeters.

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Ngọc Hoa 4 years 2021-07-27T17:51:15+00:00 2 Answers 8 views 0

Answers ( )

    0
    2021-07-27T17:52:24+00:00

    Answer:

    244mm

    Explanation:

    I₁ = 3.35A

    I₂ = 6.99A

    μ₀ = 4π*10^-7

    force per unit length (F/L) = 6.03*10⁻⁵N/m

    B = (μ₀ I₁ I₂ )/ 2πr ………equation i

    B = F / L ……….equation ii

    equating equation i & ii,

    F / L = (μ₀ I₁ I₂ )/ 2πr

    Note F/L = B = F

    F = (μ₀ I₁ I₂ ) / 2πr

    2πr*F = (μ₀ I₁ I₂ )

    r = (μ₀ I₁ I₂ ) / 2πF

    r = (4π*10⁻⁷ * 3.35 * 6.99) / 2π * 6.03*10⁻⁵

    r = 1.4713*10⁻⁵ / 6.03*10⁻⁵

    r = 0.244m = 244mm

    The distance between the wires is 244m

    0
    2021-07-27T17:52:28+00:00

    Answer:

    d = 77.5mm

    Explanation:

    The expression used for calculating the force between two parallel wires carrying currents separated by a distance is;

    F12 =µµol1I2L/2πd where

    I1 and I2 are the currents in both wires

    L is the length of the wires

    d is the separation distance

    F12 is the magnitude of the force between them.

    µo is the constant of proportionality

    The equation can be rewritten as;

    F12/L = µµol1I2/2πd

    F12/L is the force per unit length acting on each wire= 6.03×10^-5 N/m

    I1 = 3.35A

    I2 = 6.99A

    µ = 1

    µo = 4π×10^-7N/A²

    d =?

    Substituting this datas in the equation above to get the separation distance d we have;

    6.03×10^-5 =1× 4π×10^-7 × 3.35 × 6.99/2πd

    6.03×10^-5 = 4×10^-7×23.42/2d

    6.03×10^-5 = 9.37×10^-6/2d

    2d = 9.37×10^-6/6.03×10^-5

    2d = 1.55 × 10^-1

    d = (1.55 × 10^-1)/2

    d =0.155/2

    d = 0.0775m

    Since 1m = 1000mm

    0.0775m = (0.0775×1000)mm

    d = 77.5mm

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