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28 July, 18:53

A 17.0 g piece of Styrofoam carries a net charge of - 7.00 μC and floats above the center of a large horizontal sheet of plastic that has a uniform charge density on its surface. What is the charge per unit area (in C/m2) on the plastic sheet? (Include the sign of the value in your answer.) Hint

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  1. 28 July, 18:56
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    Given that,

    Mass of styrofoam = 17g=0.017kg

    Net charge is q = -7.00 μC

    Electric field of a sheet is given as

    E = σ / 2εo

    σ = charge density

    εo = permittivity of free space = 8.85*10^-12

    Also electric field is given as

    E=F/q

    The force acting on the body is its weight which is given as

    F=mg,

    Where g=9.81

    F=0.017*9.81

    F=0.16677N.

    Therefore,

    E=F/q

    E=0.16677 / - 7*10^-6

    E=-23824.29N/C

    Then,

    E = σ / 2εo

    Then, σ = E * 2εo

    σ=-23824.29*2*8.85*10^-12

    σ = - 4.22*10^-7C/m²

    σ = - 42.2*10^-6 C/m²

    σ = - 42.2 μC/m²

    The charge density is - 42.2 μC/m²
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