Two small plastic spheres are given positive electric charges. When they are 15.0 cm apart, the repulsive force between them has magnitude 0.220 N. What is the charge on each sphere (b) if one sphere has four times the charge of the other?

Video transcript

Welcome back, everybody. We are taking a look at two different glass balls here and we are going to rub them with silk so that they are now positively charged. We are told that when they are placed at a distance of 20 centimeters or 0.2 m away from each other, that there is a repelling force present of 0.28 newtons. We're also told that they are going to both be positively charged and have different charges. But that one of the charges is going to be equal to five times the other charge for so for conventions sake, what I'll do is I'll say that Q one has a magnitude of charge of Q and that Q two has a magnitude of charge of five Q. And we are tasked with finding what Q one and Q two are. And the key to that of course, is going to be finding the magnitude of charge of Q and then using these relations to find both Q one and Q two. So let's go ahead and work on finding our magnitude of charge Q first. So when we are dealing with uh electromagnetic forces, we are going to look at Kla's Law here. Klum's law states that the force is equal to Kums constant times the charge of the first particle times the charge of the second particle all over the distance between them squared. This is going to be equal to, well, I'm going to in these values right here. And we get that this is equal to K times Q times five Q all over are squared to simplify this even further. This is then equal to five A Q squared all over R squared. Let me go ahead and rewrite both sides of the formula here because we are gonna do some manipulations to isolate Q. So we have the F is equal to five kq squared over R squared. Now we want to get this Q term by itself. So I'm gonna start out by multiplying both sides by R squared over five K are squared over five K. You'll see that on the right hand side, all of these terms cancel out. We are then left with two squared is equal to fr squared over five K. Finally, to get Q by itself, we are going to take the square root of both sides yielding that Q is equal to a square root of five R squared over five A. Now that we have, oh My apologies, this is going to be fr squared over five K and square roots of that. Now that we have our formula for Q, let's go ahead and plug in all of our numbers here. You're gonna have that. This is the square root of our force. 0.28 times 0.2 the distance between them squared all over Kums constant nine times 10 to the ninth times five. When you plug this into your calculator, we get that U is equal to 4.99 times 10 to the negative seventh OMs right now that we have found Q, we are ready to go ahead and find Q one and Q two. Once again, using this relationship up here that we established earlier, the Q one is just equal to Q. So this is just going to be 4.99 times 10 to the negative seventh OMs. Q two is equal to five Q. So we have five times 4.99 times 10 to the negative seventh. And this, when you plug into your calculator, we get 2.49 times and to the negative six columns. So now we have found the charge of each glass ball which corresponds to answer choice. B. Thank you all so much for watching. I hope this video helped. We will see you all in the next one.