Two long straight parallel lines, #1 and #2, carry uniform positive linear charge densities. The charge density on line #2 is twice as great

Question

Two long straight parallel lines, #1 and #2, carry uniform positive linear charge densities. The charge density on line #2 is twice as great as the charge density on line #1. The locus of points where the electric field due to these lines is zero is

along a line between the lines closer to line #2 than line #1.

at a point midway between the lines.

along a line between the lines closer to line #1 than line #2.

along a line perpendicular to lines #1 and #2.

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Mộc Miên 4 years 2021-08-24T14:00:08+00:00 1 Answers 18 views 0

Answers ( )

  1. thienhuong
    0
    2021-08-24T14:01:31+00:00
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    Answer:

    The locus of points where the electric field due to these lines is zero is;

    Along the line between the lines closer to line#1 than line #2

    Explanation:

    The charges on the parallel lines #1 and #2 = Positive linear charge

    The charge density on line #2, λ₂ = 2 × The charge density on line #1, λ₁

    Therefore, we have;

    λ₂ = 2 ×  λ₁

    Electric field strength, E, is given as follows;

    E = \dfrac{\lambda}{2\cdot \pi\cdot \epsilon_0\cdot d}

    Therefore;

    E_1 = \dfrac{\lambda_1}{2\cdot \pi\cdot \epsilon_0\cdot d}

    E_2 = \dfrac{\lambda_2}{2\cdot \pi\cdot \epsilon_0\cdot d} = 2 \times\dfrac{\lambda_1}{2\cdot \pi\cdot \epsilon_0\cdot d}

    E₂ = 2·E₁

    E₂/2 = E₁

    E₂/(2·d) = E₁/d

    The strength of the electric field at a given distance from line #2 is 2 times the strength of the electric field from line #1 at the same distance

    Therefore the strength of the electric field will be the same at a point twice the distance from line #2 than from line #1 which is a point closer to line #1 than line #2.

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