Static Electricity Legacy Problem #9 Guided Solution

Physics problems are typically difficult for a variety of different reasons. Regardless of the reason for the difficulty, an effective problem solver adopts a consistent approach such that in every problem they're going to approach it in the same way, trusting in their skills of solving problems. Here, we would read the problem carefully and extract the numerical information from it and begin to identify the known and the unknown quantities. Here we know that we have two objects with charges q1 and q2, where q1 is a positive 3.27, mu c and q2 equal a negative 4.91 mu c. I would simply write those two quantities down and I would equate them with the variables q1 and q2, the same variables in my Coulomb's law equation. I also know that these two objects attract with a force of 0.358 Newtons. Now I'll write down F equal 0.358 Newtons, and my unknown quantity in this problem is the distance that separates the two objects. I wish to find d, the same d, in the Coulomb's law equation. Now I'll begin to identify a relevant equation for use in this problem, and quite evidently this one is going to be the Coulomb's law equation, which goes F equal k times q1 times q2 divided by d squared. And in that equation we know all quantities except for the distance. So I'm going to rearrange my equation such that it becomes d squared equal k times q1 times q2 all over the value of F. Now as I substitute into this equation I'm going to have to get my values of q substituted in in the proper unit. The value of k is 8.99 times 10 to the ninth Newtons times meters squared per Coulomb squared. And so in order to do my proper substitution I need to use not the 3.27 mu c, but rather the equivalent version in units of Coulombs. I need to take advantage of the fact that there is one Coulomb equivalent to 10 to the sixth micro Coulombs. Taking advantage of this fact I can convert the 3.27 micro Coulombs to units of Coulombs, and the 4.91 micro Coulombs to units of Coulombs as well. I'll need to divide by 10 to the sixth in order to do that. Now the next little complication in this problem is that I'm going to have to make sure that I substitute simply absolute value signs of these charges. The fact that it's positive and negative is simply the type of charge and has nothing to do with the quantity of charge. So in substituting into the Coulombs law equation I want to substitute quantities only, ignoring the plus minus type of charge that's present on the object. Now if I do all this appropriately and pay attention to good algebra skills I'll be able to solve for d squared. Once I get my value of d squared I'm going to take the square root of it and that gives me the value of d. It would be 0.635 meters or 63.5 centimeters, either expression being okay.