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12 February, 17:12

A solid sphere of radius R has a total charge Q distributed evenly throughout its volume. What fraction of the total charge is located inside a radius R/2?

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  1. 12 February, 18:17
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    Volume charge density ρ = charge / volume

    = Q / (4/3 πR³)

    total charge is located inside a radius R/2

    = volume charge density x volume of sphere of radius R/2

    = [Q / (4/3 πR³) ] x 4/3 π (R/2) ³

    = [Q / (4/3 πR³) ] x 4/3 πR³ x 1/8

    = Q / 8

    required fraction

    = 1/8.
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