If the force between two charges is F when the distance is d, what will the force between the two charges be if they were moved to a distance of 2d?

Hey guys. So hopefully we have to solve this one on your own. So we have the force between two charges and it's f. They're separated by some distance D and we're gonna have to change some of that. We're gonna have to figure out the new forces. So this is a proportional reason type problem, and we've done this before. First, let's go ahead and set up the original Coolum four. So the cool enforcing the original situation between these charges we know it's K Q one Q two divided by R squared. But in this case, instead of using that are all they're doing is just changing that out for the variable d. So I have d squared. So what's going on in situation is that we're going to move these charges to a distance of two D. In other words, we're gonna manipulate the distances so that the new distance between these two charges is just twice of whatever it was before. So now we have to figure out the new electric forces. We're just gonna go ahead, right? That the expression for that the new expression or the new cool and force is gonna be K Q one Q two. The charges remain the same, except now we just have to write in D new. The new distance between them squared. So now all we have to do is just take this expression for D new that we have and just stick it inside of that expression right there. So let's keep going. We've got the new cool, um, force is just gonna be K Q one Q two divided by and now we have toe right in the parentheses for two D and then square that it's important that you put in the two in the parentheses because remember that this squared here is going to distribute to both of these terms that are inside. So what happens is this becomes K Q one Q two divided by now. Two squared is four and D squared is just D squared. So now what happens is we've gotten this expression, and I could basically extract this little number and pull it towards the outside because it's in the denominator. So what this becomes is becomes 1/4 and then we have K Q one Q two divided by D squared. So if you take a look at this. This is the expression for F new. But this expression right here is just the original force between these two charges. So this is just the original F. So, in other words, the new force between these two charges when the distance gets doubled is 1/4 of the original force when these things were closer together. So this is basically the answer. But another way to see this kind of, uh, these kinds of proportional reason questions is you just set up their proportion. We know that the Coolum force Sorry, it's not equal. We know the Coolum force is inversely proportional to the distance between the charges. So now what happens is in these kinds of problems. Whenever you're gonna multiply the two whenever gonna multiply the distance and double it, then what happens to the electric force is it gets divided by four. Because what happens is whatever this number is, it's just gonna get squared. So, for instance, if I were to divide this distance now by three, then what happens is this gets squared and it would be multiplying the original force by nine. So whatever happens to this, you're just gonna do the opposite operation and then square this number right times two, divided by four, divided by three times nine. Alright, so that's just another way to see these kinds of problems. Let me know if you guys have any questions.

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If the force between two charges is F when the distance is d, what will the force between the two charges be if they were moved to a distance of 2d?

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