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13 April, 14:03

An uncharged, nonconducting, hollow sphere of

radius 10.0 cm surrounds a 10.0-uC charge located

at the origin of a Cartesian coordinate system. A drill

with a radius of 1.00 mm is aligned along the z axis,

and a hole is drilled in the sphere. Calculate the elec-

tric flux through the hole.

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Answers (1)
  1. 13 April, 14:11
    0
    The whole surface of hollow sphere = 4π r²

    = 4 x 3.14 x (10 x 10⁻²) ²

    = 12.56 x 10⁻² m²

    Area of the hole (both side) = 2 x π r²

    = 2 x 3.14 x (10⁻³) ²

    = 6.28 x 10⁻⁶ m²

    flux coming out of given charge at the centre as per Gauss's theorem

    = q / ε₀ where q is charge at the centre and ε₀ is permittivity of the medium.

    = 10 x 10⁻⁶ / 8.85 x 10⁻¹²

    = 1.13 x 10⁶

    This flux will pass through the surface of sphere so flux passing through per unit area

    = 1.13 x 10⁶ / 12.56 x 10⁻²

    = 8.99 x 10⁶ weber per m²

    flux through area of hole

    = 8.99 x 10⁶ x 6.28 x 10⁻⁶

    = 56.45 weber.
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