Static Electricity Legacy Problem #6 Guided Solution

If a balloon is rubbed against human hair, it will become charged. Electrons will be transferred from the less electron-loving hair to the more electron-loving balloon. And the balloon becomes charged. If this is done with two balloons, both balloons will become charged with like charge and as such will repel each other. In this problem, we are told that two balloons are charged in such a manner, transferring 2.1 times 10 to the 12th electrons from the hair to the balloon. Given this information, we should be able to calculate the quantity of charge on each balloon. Doing so involves using the idea that each electron has a charge of 1.6 times 10 to the negative 19th coulombs. So if you have 2.1 trillion of these electrons, then what you need to do is take this number 2.1 times 10 to the 12th and multiply it by the charge of a single electron. Doing so gives you a value for the quantity of charge on each balloon of 3.36 times 10 to the negative 7th and the unit is a coulomb, abbreviated C. Now these two balloons with that charge are held a distance of 58 centimeters apart. The centimeters is important, we will talk about that later. Now what we wish to do in part B of this problem is find the force of repulsion between these two balloons with these charges and this distance of separation. That involves using the Coulomb's Law equation, F equals k, the Coulomb's Law constant, times q1 times q2 divided by the distance squared. Now the value of k, the proportionality constant in the equation, is 8.99 times 10 to the 9th newtons times the meter squared per coulomb squared. So as we substitute values of q1 and q2 and d into this equation, we have to make sure that our units of coulomb squared and meter squared cancels and we are left with a newton as the unit of force on the answer. So to do that we have to make sure that q1 and q2 are in coulombs, and they currently are, and that the d is in units of meters and it is stated in centimeters. So we need to take the 58 centimeters and think real hard about how to convert that to units of meters. Doing the conversion takes advantage of the fact that we would know that there are 100 centimeters in one meter. And using that information we should be able to convert to meters. Substitute the value of distance into the equation in units of meters, make sure it gets squared, and you can calculate your answer.