Two charges originally separated by a certain distance are moved farther apart until the force between them has decreased by a factor of 10.

Question

Two charges originally separated by a certain distance are moved farther apart until the force between them has decreased by a factor of 10. (a) Is the new distance (1) less than 10, (2) equal to 10, or (3) greater than 10 times the original distance? Why?

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Ben Gia 3 years 2021-09-05T14:39:49+00:00 1 Answers 14 views 0

Answers ( )

  1. ngochoa
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    2021-09-05T14:41:30+00:00
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    Answer:

    New distance is less than 10.

    Explanation:

    The force acting between two charges is given by :

    F=k\dfrac{q_1q_2}{d^2}

    k is the electrostatic constant

    d is the distance between charges

    If two charges originally separated by a certain distance are moved farther apart until the force between them has decreased by a factor of 10, F'=\dfrac{F}{10}  

    New force is given by :

    F'=k\dfrac{q_1q_2}{d'^2}

    \dfrac{F}{10}=k\dfrac{q_1q_2}{d'^2}

    d'=\sqrt{10} \times d

    So, the new distance is \sqrt{10} times the original distance i.e. the new distance is less than 10 times the original distance. Hence, the correct option is (1).

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