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23 September, 04:19

A square plate of copper with 55.0 cm sides has no net charge and is placed in a region of uniform electric field of 82.0 kN/C directed perpendicularly to the plate. a. Find the charge density of each face of the plate. b. Find the total charge on each face.

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  1. 23 September, 06:21
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    Answer

    given,

    Side of copper plate, L = 55 cm

    Electric field, E = 82 kN/C

    a) Charge density,σ = ?

    using expression of charge density

    σ = E x ε₀

    ε₀ is Permittivity of free space = 8.85 x 10⁻¹² C²/Nm²

    now,

    σ = 82 x 10³ x 8.85 x 10⁻¹²

    σ = 725.7 x 10⁻⁹ C/m²

    σ = 725.7 nC/m²

    change density on the plates are 725.7 nC/m² and - 725.7 nC/m²

    b) Total change on each faces

    Q = σ A

    Q = 725.7 x 10⁻⁹ x 0.55²

    Q = 219.52 nC

    Hence, charges on the faces of the plate are 219.52 nC and - 219.52 nC
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