WEBVTT 00:00:00.091 --> 00:00:02.742 This is College Physics Answers with Shaun Dychko. 00:00:03.148 --> 00:00:05.588 We're going to find the ratio of the electrostatic force 00:00:05.708 --> 00:00:09.348 to the gravitational force between two electrons 00:00:10.074 --> 00:00:12.097 and then do it again for between two protons. 00:00:12.645 --> 00:00:17.051 So the electrostatic force is Coulomb's constant times the two charges, 00:00:17.051 --> 00:00:18.651 both of which are the elementary charge 00:00:18.851 --> 00:00:22.022 and so we square them, square the elementary charge, 00:00:22.474 --> 00:00:24.611 and divide by the distance between the two charges, 00:00:25.325 --> 00:00:27.977 and the gravitational force is the gravitational constant 00:00:27.977 --> 00:00:31.228 times the mass of each electron multiplied together, 00:00:31.491 --> 00:00:33.005 divided by the distance between them squared. 00:00:33.794 --> 00:00:38.251 The ratio of these two forces is going to be the electrostatic force 00:00:38.542 --> 00:00:40.188 divided by the gravitational force. 00:00:40.268 --> 00:00:42.302 Now instead of dividing a fraction by a fraction, 00:00:42.302 --> 00:00:45.371 I'm going to multiply by the reciprocal of this fraction, 00:00:45.640 --> 00:00:48.245 so multiplying by r squared over g m e squared. 00:00:49.342 --> 00:00:54.371 This works out to k q e squared over G m e squared and the r squareds cancel. 00:00:55.497 --> 00:00:56.765 Then we substitute in numbers 00:00:57.017 --> 00:01:00.857 and we have the Coulomb's constant times the elementary charge squared, 00:01:00.857 --> 00:01:04.714 divided by the gravitational constant, times the mass of an electron squared. 00:01:05.074 --> 00:01:09.497 We get 4.16 times ten to the forty-two which is a very massive number. 00:01:11.085 --> 00:01:13.554 This means electrostatic force is way bigger 00:01:13.851 --> 00:01:16.188 than the gravitational force for electrons. 00:01:18.160 --> 00:01:22.417 Now when it comes to protons, the expression is basically going to be the same 00:01:22.417 --> 00:01:25.291 but we'll have mass of a proton down here instead of mass of an electron. 00:01:25.514 --> 00:01:27.685 So we substitute in all the same numbers as before 00:01:27.685 --> 00:01:32.365 but now the mass of electron which was 9.11 times ten to the minus thirty-one kilograms, 00:01:32.731 --> 00:01:37.062 is replaced instead with 1.67 times ten to the minus twenty-seven kilograms, 00:01:37.062 --> 00:01:38.051 mass of a proton. 00:01:38.302 --> 00:01:40.777 This works out to 1.24 times ten to the thirty-six 00:01:40.777 --> 00:01:44.622 is the ratio of the electrostatic force to the gravitational force for protons. 00:01:45.131 --> 00:01:49.320 The reason these ratios are different is because the masses are different.