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# A charged particle $A$ exerts a force of 2.62 $\mathrm{N}$ to the right on charged particle $B$ when the particles are 13.7 $\mathrm{mm}$ apart. Particle $B$ moves straight away from $A$ to make the distance between them 17.7 $\mathrm{mm}$ . What vector force does particle $B$ then exert on $A$ ?

## $1.57 \mathrm{N},$ to the left

### Discussion

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##### Christina K.

Rutgers, The State University of New Jersey

LB

### Video Transcript

So let's say you have two charges a NB here at the top or a tablet and they're separated by 13.7 meters. If the force between them is 2.62 years and then you separated some more to 17.7 meters have millimeters. What is the force on A and what direction? So originally the forces felt in the right direction. Let's have it is in that direction and we don't have to be to 1 62 And because there's two charges we can use, cool on the block. Who lost says that Kay times the case that composite Q A. So the charge of a Q B the charge of B divided by are that this is between the two from A to B squared and so that we know that are right here is 13.7. So we use that information to solve the problem here. So now what we do is really this. We don't solve for this right away we do a ratio. So we say, What is f of a the force on the divided by the force on me previously that we knew until because there's equal and opposite force is the force on A is going to be the same as a force on be. So that's what you can just like this. And so we know that the force of A is obviously as we know. Okay, you a SUV time ready by the distance from a to B squared and it's everything here are to be It's just weird. And so these two don't change because they're constant, right? Then we'll change with the problem so they end up cancelling out, cross it up. So what? Those changes the ars the distances so you can rewrite this racing gonna end up being more on older than you are. So just write our news R N Square. What about Warren Older? Our goal for old squared. And you could just rewrite that as our old squared over our news word. Hold squared. All right. New so that you can solve for that number. And that's when you zero point about the open in the Bible, 0.59 And so you can reorganize this because you know this number from before, right? You know it's over here, so solving for half A you get that F A is equal to 0.5 Times B, which is about 1.57

University of British Columbia
##### Christina K.

Rutgers, The State University of New Jersey

LB