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26 December, 20:41

A solid nonconducting sphere of radius R carries a uniform charge density throughout its volume. At a radial distance r1 = R/4 from the center, the electric field has a magnitude E0. What is the magnitude of the electric field at a radial distance r2 = 2R?

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  1. 26 December, 22:22
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    Given that,

    Sphere of radius R

    At radial distance ¼R it has an electric field of Eo

    Magnitude of electric field E at r=2R

    Solution

    electric field is given as

    E=KQ/r²

    Now at R,

    E=KQ/R²

    When, at r=R/4 inside the sphere is given as

    Eo=kQ/R³ • R/4

    Eo=kQ/4R²

    When, r = 2R

    Then,

    E=kQ / (2R) ²

    E=kQ/4R²

    Comparing this to Eo

    Then, E=Eo

    Then, the electric field at r=2R is equal to the electric field at r=R/4
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