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5 January, 01:20

A very long, straight wire has charge per unit length 3.50*10^-10 C/m. At what distance from the wire is the electricfield magnitude equal to 2.90 N/C?

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  1. 5 January, 04:00
    0
    r = 2.17 m

    Explanation:

    Conceptual Analysis:

    The electric field at a distance r from a charge line of infinite length and constant charge per unit length is calculated as follows:

    E = 2k * (λ/r) Formula (1)

    Where:

    E: electric field. (N/C)

    k: Coulomb electric constant. (N*m²/C²)

    λ: linear charge density. (C/m)

    r : distance from the charge line to the surface where E calculates (m)

    Known data

    E = 2.9 N/C

    λ = 3.5*10⁻¹⁰ C/m

    k = 8.99 * 10⁹ N*m²/C²

    Problem development

    We replace data in the formula (1):

    E = 2*k * (λ/r)

    2.9 = 2*8.99 * 10⁹ * (3.5*10⁻¹⁰/r)

    r = (2*8.99 * 10⁹*3.5*10⁻¹⁰) / (2.9)

    r = 2.17 m
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