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Question
  1. Find the ratio of the electrostatic force to the gravitational force between two electrons.
  2. Will this ratio change if the two electrons are replaced by protons? If yes, find the new ratio.
Question by OpenStax is licensed under CC BY 4.0.
  1. $4.16\times 10^{42}$
  2. Yes, the ratio will be different due to the different mass of the protons. $1.24\times 10^{35}$
Solution Video

OpenStax College Physics for AP® Courses Solution, Chapter 18, Problem 30 (Test Prep for AP® Courses) (1:45)

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Video Transcript
This is College Physics Answers with Shaun Dychko. We are going to find the ratio of the electrostatic force to the gravitational force between two electrons so the gravitational force will be the gravitational constant times the mass of the two electrons multiplied together divided by the distance between them squared and assuming they are separated by the same distance so r does not need a subscript between these two scenarios, the electrostatic force then is going to be Coulomb's constant k times the elementary charge squared divided by that same distance between them squared. So we take the ratio of these by dividing them so we have electrostatic force divided by gravitational force and so we have copied the electrostatic force here and dividing a fraction by a fraction is a bit confusing so I prefer to multiply by the reciprocal of the denominator so I am multiplying by this gravitational force flipped over and the r squared's cancel and the ratio then is Coulomb's constant times the elementary charge squared divided by the gravitational constant times the mass of an electron squared and this is 4.16 times 10 to the 42. So the electrostatic force is 42 orders of magnitude greater than the gravitational force. And in part (b), we are asked to find this ratio for two protons and the ratio will be different so yes it will be different and the difference is that this factor here is going to be the mass of a proton now instead of the mass of an electron and the mass of a proton is four orders of magnitude greater than that of an electron and we end up with a ratio of 1.24 times 10 to the 35.