In which direction will the −1 C charge move? If it has a mass of 10 g, what will its initial acceleration be?

left; 6.2×$$10^{13}$$ $$m/s^{2}$$

In which direction will the −1 C charge move? If it has a mass of 10 g, what will its initial acceleration be?

How's it going, guys? I hope you were able to try this one on your own. So we have to find out what direction this negative one Coolum charge that's in the middle right here is going to move. And if we're given its mass, what is its initial acceleration going to be? All right, So in order to figure out which direction it's going to move, let's go ahead and take a look at what the forces acting on this thing are. So we've got this to cool in charge here on the right, and this negative one cool in charge. So, in other words, this is going to exert a attractive force, right? Because they are unlike charges in this direction. I'm gonna call this F two, and this one Coolum charge is also going to exert an attractive force over here because again, there, unlike charges, we have a positive and a negative. I'm gonna call that F one, and in order to figure out which one is going toe win, Basically, I actually have to figure out what the Net Force is. So what is the Net force? Well, we're dealing with cool OEMs law. We know that any two charges have Que que que Oops! I got K Q one Q two over R squared. So all we have to do is just compare the Coolum forces from each one of the pairs of charges and figure out which one is stronger. So is F two or F one. We know that F Net is just basically going to be f two plus F one and we're gonna go ahead and choose a direction right for one of these things. Okay, so let's go ahead and figure out what F two is. F two is basically going to be the que constant, which is a 0.99 times 10 to the ninth. And then we also have the product of the two charges. I've got 22 and one now, why didn't I plug in the negative sign? Because again, let's just forget about the direction. Forget the negative sign. We're gonna pick that direction after the fact, and we want the distance between them squared. OK, Well, the distance between them is going to be well not 10. 10 centimeters is the whole entire distance. And if this is four, this has to be six centimeters. In other words, we're gonna use 0.6 and square that. All right, so if you go ahead and work this out, this force right here is gonna be five times 10 to the 12th. So this is five times 10 to the 12th. Newton's pointing in that direction. Let's just go ahead, do the same exact thing for F one. So F one is going to be 8. 99 times 10 to the ninth. Now, we've got the two charges involved. We've got a one and a one Coolum charge again. Forget about the negative sign, and then we're gonna have the distance between them squared 0.4 square. Right? Because remember these things, Aaron. Centimeters that have to be in meters. So just just in case you were wondering, All right, so if you work that out, you should get 5.62 times 10 to the 12th. All right, so this is 5.62 times 10 to the 12th. All right? And now, if we look at them, we can clearly see that the net Force we're gonna choose a positive and negative direction is going to be f two plus F one. Okay, well, this direction is going to be positive. So now you're just gonna go ahead and choose your own direction to be positive. And what that means is that if we choose the right to be positive and our answer ends up being negative, then the net force points in the negative direction. By the way, if you just chose the opposite direction, we positive your answer should be the same. But you're just gonna have the opposite sign. So physics is works out that way. So it doesn't really matter which one. You which one? You choose to be positive as long as you're consistent. All right, so the net Force is just going to be five times 10 to the 12th on. Then it's gonna be so I'm gonna call this negative right here, minus 5.62 times 10 to the 12th. And if you work this out, you should get a net force that is equal to, uh let's see, I got negative 6.2 times 10 to the 11th, and that is going to be in Newton's. Okay? Yeah. So I've got 10 6.2% minus 11. Notice how I've gotten a negative sign here. So what this negative sign means again is that this thing points to the left. If you have chosen your left direction to be positive, you would have gotten this answer to be positive because it points to the left. The physics is still the same. Just the sign just means the direction. So that's basically it for part a. Let's go ahead and take a look at part beat. So Part B now is we're supposed to figure out what the acceleration is. So we've got enough force. How do we get acceleration from force? We always get their using f equals m A. So f equals m A. So that means that the acceleration is going to be the force divided by the mass. So we have the mass. This the mass. It was just equal to 10 g. So that means that the acceleration is just the force, which is, and we're just gonna use the magnitude now that the negative direction doesn't matter anymore. So 6.2 times 10 to the minus 11 divided by 0. So that means the acceleration is gonna be 6.2 times 10 to the 13th. And that's in meters per second squared. All right, so that is the acceleration, the initial acceleration of this test charge of this one. Cool in charge or whatever. Let me know if you guys have any questions with that.

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In which direction will the −1 C charge move? If it has a mass of 10 g, what will its initial acceleration be?

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