Static Electricity Legacy Problem #24 Guided Solution

Any two objects which are charged will interact electrically with one another in order to exert attractive or repulsive forces upon each other. Here in this question we are given three charges which lie along a line and we are asked to calculate the net electric force acting upon one of the charges, the charge q1. There are two electric forces acting upon q1. One of them is the force of interaction between q2 with q1 and the other is between q3 with q1. We'll call these two forces F2 on 1, the force of charge 2 on charge 1 and F3 on 1, the force of charge 3 on charge 1. We can calculate the magnitude of these two forces if we simply use Coulomb's law individually for objects 1 and 2 and then individually for object 1 and 3. Now in the problem two of the objects are charge positive objects 1 and 2 and so as we go to calculate the force on object 1 it will be a repulsive force pushing object 2 and pushing object 1 towards the left. Object 1 and 3 are positive and negative respectively and so their interaction is the one that is described as attractive which means that object 3 pulls object 1 towards itself, towards the right. So as we go to determine the direction of the two forces we simply use the ideas that opposites attract and likes repel. Now let's get down to calculating the magnitude of the force on object 1 caused by object 2. What we do is go K, the Coulomb's law constant, 8.99 times 10 to the 9 multiplied by Q1 multiplied by Q2 and those charges are given there, divided by the distance of separation between them squared. Now that separation distance is 5 centimeters. We need to enter it into the equation as 0.05 meters in order to get units to cancel and get the unit on force to be the newton. In doing so I end up calculating a value of 0.7192 newtons and leftward I can simply round that to three significant digits. Now I need to do the same thing for calculating the magnitude of the force of charge 3 on charge 1 and in doing so I am going to have to substitute charge values into the equation. Now the equation calls for the quantity of charge not the type and so I can ignore the fact that Q3 is a negative charge and its quantity is negative, 8.0 times 10 to the negative 7th, for after all the negative part of that simply indicates the type of charge. So I would be going the value of K again, 8.99 times 10 to the 9th multiplied by 5 times 10 to the negative 7th multiplied by 8 times 10 to the negative 7th and notice I've skipped the negative 8 times 10 to the negative 7th. I divide all that by the distance squared and the distance between charge 1 and charge 3 is actually 13 centimeters. It's the d1 distance plus the d2 distance. So that's 0.13 meters. That must be squared and when I'm done I calculate the charge of F3 on 1, it's 0.2128 newtons. Final part of the problem is I have to calculate the magnitude and direction of the net electric force. That is I have to add these two force vectors with one going to the left and the other going to the right. I typically simply subtract the smaller one from the larger one whenever they are going in opposite directions such as this and I end up with 0.5064 newtons. I can round that to three digits.