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2 September, 09:39

A spherical shell contains three charged objects. The first and second objects have a charge of - 14.0 nC and 31.0 nC, respectively. The total electric flux through the shell is - 533 N ⋅ m 2 / C. What is the charge on the third object?

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  1. 2 September, 09:42
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    The charge on the third object is - 21.7nC

    Explanation:

    From Gauss's Law

    Φ = Q/ε₀

    where;

    Φ is the total electric flux through the shell = - 533 N⋅m²/C

    Q is the total charge Q in the shell = ?

    ε₀ is the permittivity of free space = 8.85 x 10⁻¹²

    From this equation; Φ = Q/ε₀

    Q = Φ * ε₀ = - 533 * 8.85 x 10⁻¹²

    Q = - 4.7 X 10⁻⁹ C = - 4.7nC

    Q = q₁ + q₂ + q₃

    - 4.7nC = - 14.0 nC + 31.0 nC + q₃

    - 4.7nC - 17nC = q₃

    - 21.7nC = q₃

    Therefore, the charge on the third object is - 21.7nC
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