Two points charges are brought closer together,increasing the force between them by a factor of 25.By what factor wa their separation decrea

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Two points charges are brought closer together,increasing the force between them by a factor of 25.By what factor wa their separation decreased?

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Thành Đạt 3 years 2021-07-21T22:04:09+00:00 1 Answers 2 views 0

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  1. linhdan
    0
    2021-07-21T22:05:11+00:00
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    Answer:

    The separation between the charges was decreased by a factor of 0.2

    Explanation:

    The Coulomb’s force between two charges is given by;

    F = \frac{kq^2}{r^2} \\\\let \ kq^2 \ be \ constant\\\\F_1r_1^2 = F_2r_2^2\\\\r_2^2 = \frac{F_1r_1^2}{F_2} \\\\increasing \ the \ force \ between \ them \ by \ factor \ of \ 25\\\\(F_2 = 25F_1)\\\\r_2^2 = \frac{F_1r_1^2}{25F_1}\\\\r_2^2 = \frac{r_1^2}{25}\\\\r_2 = \sqrt{\frac{r_1^2}{25} }\\\\ r_2 = \frac{r_1}{5}

    r₂ = 0.2r₁

    Therefore, the separation between the charges was decreased by a factor of 0.2.

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