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Which of the following is false?
  1. If the charge of one of the particles is doubled and that of the second is unchanged, the force will become 2F.
  2. If the charge of one of the particles is doubled and that of the second is halved, the force will remain F.
  3. If the charge of both the particles is doubled, the force will become 4F.
  4. None of the above.
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Solution Video

OpenStax College Physics for AP® Courses Solution, Chapter 18, Problem 26 (Test Prep for AP® Courses) (1:11)

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This is College Physics Answers with Shaun Dychko. We suppose that the electrostatic force between two charges is F and here's a formula for that: it's the Coulomb constant times one charge multiplied by the second charge divided by the distance between them squared. So we keep that in mind as we figure out which of the following is false? (a) If the charge of one of the particles is doubled and that of the other is unchanged, the force will become 2 times F certainly because if this is multiplied by 2 then that means F in total is multiplied by 2 so that is correct so that is not false. (b) If the charge of one of the particles is doubled and that of the second is halved, the force would remain the same and that's true as well; if q 1 gets doubled that factor will be canceled by the one-half factor in the second charge and there will be no change so this is true. If the charge of both particles is doubled, the force would become 4 times what it was and that's true as well because if you have a factor 2 times here and a factor 2 times there that's gonna make a total of 4 and the answer is (d): none of these are false.