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Two charges lie in a line along the x axis. Charge 1is q1 = 1.1 C and charge 2is q2 = 2.05 C. They areeach a distance of d = 0.031 m fromthe origin.What is the dist...

Question

Two charges lie in a line along the x axis. Charge 1is q1 = 1.1 C and charge 2is q2 = 2.05 C. They areeach a distance of d = 0.031 m fromthe origin.What is the distance on the x-axis from the originat which the electric field will be zero. Give your answer inmeters.

Two charges lie in a line along the x axis. Charge 1 is q1 = 1.1 C and charge 2 is q2 = 2.05 C. They are each a distance of d = 0.031 m from the origin. What is the distance on the x-axis from the origin at which the electric field will be zero. Give your answer in meters.



Answers

Two charges, $-3.0 \mu \mathrm{C}$ and $-4.0 \mu \mathrm{C},$ are located at $(-0.50 \mathrm{~m}, 0)$ and $(0.50 \mathrm{~m}, 0),$ respectively. There is a point on the $x$ -axis between the two charges where the electric field is zero. (a) Is that point (1) left of the origin, (2) at the origin, or (3) right of the origin? (b) Find the location of the point where the electric field is zero.

So in this question they tell us that we have a potential from at a distance, some distance from a point charge of 4.98 fold Sofia's 4.9 a bull's eye. And we're also told that the electric field is 12 volts per meter in our goal is to get the charge and the distance to the point charge. So here's the point charge. And if the electric fields positive, I would say that this is gonna be a positive charge. And then here is the position that we're looking at. So what we want to use is the formulas E equals que que over r squared. And then V is equal to K Q over our and then our goal is to get this. Q. I meant to use it capital or both. Kappler both negatives all go ahead and correct that just in case that creates any confusion. So, yeah, so we can see that the electric field is just the potential multiplied by one over R. So you can say that E is equal to, um V divided by our because it just has this extra factor of our. So if we have e we have V the waking up that are is equal to me or excuse me V divided by me by cross multiplying. So, uh, it's hoping these would be easier to divide but 4.9 a divided by 12 mr 415 meters and then we can go ahead and sell for a Q. And so, um, based on this one, So go ahead and block box this before it gets too confusing. So here's our R and then, um, we can sell for a Q because Q is equal to B r o ver que. Because the nine in 10 of the nine and some to go ahead and plug in this fee for 0.98 times is our and then we want to divide by K nine times 10 to the nine. So I got 2.30 times 10 to the minus 10. Coombs is there anything else is problem ones and then the electric field is directed away from the point charge. So this isn't the answer for B A and then for see its way

So in this problem, we're asked to consider two scenarios where we have two charges, Um, that are some distance d apart on day. In the first scenario, they have the same charge and then the second they have opposite charges on we're being asked to determine if there any points along the line between these two charges where the potential is zero or the electric field to zero. So basically this problem we're looking at, if there is any relationship between the potential and the electric field when there's zero. So, uh, if you wanna just do ah recap to find the total potential What that is is basically just a sailor scaler, some and all the potentials while the electric field, the net electric field is going to be a vector sum of two fields. So what does this practically mean? So basically, the potential is only going to be equal to zero If one charge is negative and the other is positive and theoretic field. Uh, that's only going to be equal to zero. Um, if the fields cancel each other out. So if they're going in opposite directions, which means Q must have the same charge So these air the scenarios where we'll get a potential of zero and a net electric field of zero. So if we look at scenario, one on the first part of this question is determine whether there are any points where the potential is zero. Since we're looking at two charges with same charge, we know that there's gonna be no point where, ah, we get V equals zero because they are of the same charge. And now, for part two of this problem are asked to determine if there's any point along this line where the electric field is zero. So on this line between the two charges, we have the electric fields that's going in opposite directions, and the only point where their magnitude is going to be equal is at the midpoint at D equals two. So we'll say at the midway point. Mhm. We can write that as deep, too. That is where the electric fields it's going to be equal to zero. But there's still no point at which the potential is going to be equal to zero is just because the electric fields zero does not mean that we have at the potential equal to zero at that point. So now we're going to do the same exercise. But just with the scenario where we have, unlike charges, So we have a positive and a negative, and as we established before, we get a potential of zero if the charges are, uh, different. So between the two charges, um, at these two potentials have equal magnitude and opposite signs at the midway point. So that means we have the equal to zero at the midway, which would be de over to on this little graph that we've drawn. But at that point at that midway point in scenario, be, uh, we would not have theorem trick field equal to zero because thief fields are going to point in the same direction. And because it's a vector some, that means they won't cancel out. So that kind of explains part two of this scenario. We're not gonna have any point that that the electric field is actually equal to zero. Uh, because no matter where it is along this line, uh, the field near one charge is going to be slightly larger than the field due to the other charge on the field. They're going to be pointing in the same direction, um, along this entire line between the charges, so you won't be able to see her anywhere. And so basically what this exercise is showing us is that just because the electric field is equal to zero does not mean the potential will be equal to zero or vice versa.

Hello, everyone here it is giving to charges off equal magnitude on help after distance d apart. So here, Cuban, it's fair to you, too. It's starting Q. And they are help. And after that, Sprint's de apart. Consider only points on the line. Passing through would chart it. But it Yeah, you want butto have same sex, same site when all the points if there are any average fight the point at which But I can tell it's to be a hero on electric feelings to be, you know And second But if you want and beautiful having a project site, then find the point. Edwidge, What they said to be a hero on electric field will be zero. We started with it. If we take any point b at distant away from Cuba, then potential at people be okay you upon x Okay, you d minus X. That is take you. If we take common, it will be X in tow, B minus sex. So you will get B minus X, but let's x so que que upon be upon at window B minus X But ever been, maybe the bed to affect what angel never video bright paper. Very you off X. What ain't shit now about a video? But if we see the electrically, it's off like coverage. This issue the system. If we take that point, be electric field Goto. This will be he wouldn't And you know this. It will be a toe so that electric feel at peace and rep tradition of this. So both having a portrait direction the human right? Okay, you are born excess. Quit minus I can Okay you up one this distance don't understand is d So it will be B minus x holy square. And this is you don't for electric field movie zero Take us square. You made a comment so we can write one upon Access square My let's burn upon do u minus X square. Well, you don't. This quantity can not be, you know, But this may be a little I have taken the project sense of this will be negative and this must be positive to the minus one upon exit square. But let's burn upon do u minus active square toe zero so we can see bon upon Access square is going toe bone upon B minus active script. So on solving it. We can right axis called B minus X. So for excess car tow by tow electric field, maybe Jiro. So bad to charges having the same side. That is a pretty maybe ego at the midpoint. But what? They will never be dio so we can conclude. Right? Importantly, Off touch on therapy. What? Same polarity off judge. There would not be any points. Any point at which. What do you tell? A zero but electric feel? Maybe Jiro electric field will be zero Not, maybe we'll video at the midpoint. No, be up to analyze the second kids. What? The charge is heavy. A budget quality. Suppose one. It's positive and that is negative. These the restraints if we take people extra stint of it from this judge, the potential at me If the media, it will be okay. Two opponents on Don't do this. It will be okay. My rescue upon do U minus six. So this baby zero on solving you can say, But what Intel will be zero view, right? You buy eggs, it's goingto Thank you. Bye. D minus six on simplify exits for Toby minus X. So X is going to divide toe. So at the midpoint. So at this, will you? What? Angel is zero? No. If we see the electrically at any point, do do this car. It will be in this direction. And you do this chart also in the same direction. The total field at three point Really? He went blessed toe. You won't get imbedded in it. Que que? Upon actor square, I kept you do candidate an escape you upon B minus x holy square I kept That means you made right. Thank you one upon exit square. Do you mind this access square I kept on solving it. You can write it this to be so whatever may be the value objects electrically never do whatever And were you up? X electric clean cannot video So for second part of our until it's unset off b But if both charges having a budget site then at the midpoint What I tell you zero. But there would not be any point at which electric real job is you. So this is the answer Par. This problem. Thanks for putting it

I to start this question, we must know a little bit about electric fields and electric potentials for the electric field is a back to quantity and the next minute to feel due to individual charges is equal to the vector sum electric fields in mercy. On the other hand, the electric potential it's scary quantity and the total potential d to the two charges equal to the son of their individual potentials. Soto answer part ai. So in part A and we also have to answer part by party. So the electric potential due to the two positive charges cannot be zero as the electric potential to each positive charge This positive therefore attention difference are they can never be, uh there is no point where the electric potential is zero day to the two positive charges. So the potential can never be zero because of the two positive charges. And I mean just to cars, and this is a not equal sign just to show the electric potential. All right, let me electric potential is what's not fishing potential notation. The electric potential location is actually not P instead of be So I get that right. Yeah, beef revolt. Obviously. I know for part two in party Support II on the electric field. Exactly at midway between the two part positive charges there. So that is the answer. So add Midway. Yeah, hold on. I'll explain this in a bit. Midway. The potential you This is because at that point, the electrics used to both charges are equal in magnitude and in opposite directions. So, director, some actually cancel. Cancel them up in the vector quantities, taking the consideration both magnitude and direction. All right, so not to move to part B. There are two parts in part B. So the first point, the electric potential due to a positive charge is positive and the electric potential detour negative charges negative. So, in the case of two positive charges separated by the same distance electric potential exactly between the charges. Zero. So what? It once again the midway at the midway point between two charges there is no potential in the charge, is zero. This is because electric potentials due to both the charges have equal magnitude, but opposite sign our opposite direction. So to act a part to a party. The electric field between the charges is not syrup. So it is not zero because the electric fields are directed in the same direction at every point between the charges in the outside region. Also, the Net electric field is not there because the magnitude of the electric field, due to the nearest charge, is always greater than that of the farthest. So that is it for this one, this is more often then.


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