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10 March, 02:57

A solid conducting sphere with radius R that carries positive charge Q is concentric with a very thin insulating shell of radius 2R that also carries charge Q. The charge Q is distributed uniformly over the insulating shell. Find the magnitude of the electric field in the region 02R. Express your answer in terms of the variables R, r, Q, and constants π and ε0.

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  1. 10 March, 05:52
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    Gauss Law relates the distribution of electric charge to the resulting electric field.

    Applying Gauss's Law,

    EA = Q / ε₀

    Where:

    E is the magnitude of the electric field,

    A is the cross-sectional area of the conducting sphere,

    Q is the positive charge

    ε₀ is the permittivity

    We be considering cases for the specified regions.

    Case 1: When r < R

    The electric field is zero, since the enclosed charge is equal to zero

    E (r) = 0

    Case 2: When R < r < 2R

    The enclosed charge equals to Q, then the electric field equals;

    E (4πr²) = Q / ε₀

    E = Q / 4πε₀r²

    E = KQ / r²

    Constant K = 1 / 4πε₀ = 9.0 * 10⁹ Nm²/C²

    Case 3: When r > 2R

    The enclosed charge equals to Q, then the electric field equals;

    E (4πr²) = 2Q / ε₀

    E = 2Q / 4πε₀r²

    E = 2KQ / r²
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