Static Electricity Legacy Problem #14 Guided Solution

In physics, we like to algebraically manipulate our physics formulas in order to solve for an unknown quantity, but physics equations are a whole lot more than that. Physics equations can be guides to thinking about how a variation in one of the variables within the equation can affect another variable. This question pertains to Coulomb's law equation and how a variation in the distance would affect the force of electrical attraction or repulsion between two objects, two charges, Q1 and Q2. Here we're given the force when the objects are a distance d apart. That force is 8.0 times 10 to the negative 4th Newtons. That force depends upon three quantities, the quantity of charge on object 1, the quantity of charge on object 2, and the distance between them. If you were to change any of those three variables, you would as a result change the force of attraction. It would no longer be 8.0 times 10 to the negative 4th. So in this problem, we're asked, what happens if you double the distance? That's part A of this question. Well, if you were to double the distance, what you would be doing is quadrupling the d squared variable that's in the denominator on the right side of the Coulomb's law equation. And as a result, if you quadruple the denominator, you're going to make the left side of the equation 1 4th the original value. So 1 4th of 8.0 times 10 to the negative 4th Newtons is going to be 2.0 times 10 to the negative 4th Newtons. Now if you triple the distance, you make it three times further apart, you're going to make that d squared quantity go up by a factor of 9. That means the denominator on the right side is going to increase by a factor of 9, causing the force on the left side of the equation to decrease by a factor of 9. So if you take the 8.0 times 10 to the negative 4th Newtons and divide by 9, you'll get on the order of 8.9 times 10 to the negative 5th Newtons. We need to continue this for all four parts of this question. If you half the distance, you make d squared get smaller by a factor of a 4th. That's 1 half squared, which means that you're going to make the left side of the equation get bigger by a factor of 4. It's going to be 4 times bigger if the denominator goes down by a factor of 1 4th. The final part of this problem is when you double the distance, which would in itself make the force go down by a factor of 4, but you also change the charge on both of the objects. If each object has its charge doubled, then the q1 and the q2 quantities are going to get bigger by a factor of 2, and the product q1 times q2 gets bigger by a factor of 4. And as a result, these two changes, or three changes, actually balance each other out. There's no overall effect upon the force of electrical attraction.