the-figure-below-shows-three-point-charges-all-positive-if-the-net-electric-force-on-the-center-char

Question

The figure below shows three point charges, all positive. If the net electric force on the center charge is zero, what is the value of $y / x ?$
Graph cannot copy
(A) $\frac{4}{9}$
(B) $\sqrt{\frac{2}{3}}$
(C) $\sqrt{\frac{3}{2}}$
(D) $\frac{3}{2}$

Vishal Gupta · Accepted Answer

Hi way given problem. There are three point charges as shown in the figure. Suppose at point A. This is a charge plus studio, then at another point. B. This is a charge plus three Q and at the central point C, this is a charge plus Q. The distance between A and C is given US X and the distance between B and C is given us why. And it is said that the force, the total electrostatic force acting at this model charge, is zero. It means the electrostatic repulsion experienced by this middle charge means FFC due to a should be equal toe the repulsion experienced by the same charge Do do the charge would at be means f fc do toe be so we can say f exceed uto a is equal toe f at sea Do Toby now using columns law, we know the expression for electrostatic force. Acting between the two charges is K, where K is a constant whose value is one by four pi epsilon Not, but as here it will be canceled from both sides. So we are using just k in place of this constant. So here it becomes k into Cuban into Kyoto by our square. For Cuban, this is cute. The charge kept here at sea and for you to this is Tokyo. The charge put at a and the distance between them is X squared. Now for F exceed you, Toby. Okay. Again then This is que and this is treat you the distance between them is the square off. By canceling the similar terms on both the sides K with Kate Thank you with the Q and then this Q also with this queue. So the remaining will be in the left hand side. This is to buy excess square in the right hand side. This is three by White Square. Or we can say why square by X square is equal to three by two. So finally, why by X comes out of the square root off three by two hands We can see option C is correct. Thank you

Shoukat Ali · Answer

in the first part of this problem, we have to find a very for you, too. You, for the potentially. You at the center of the square. So we need to find this are cute, too, as the total potentially zero so we can ride zero equals toe the potential due to charges Q. On Q one you wanted by our one, plus the potential due to charges to which is the cause to catch two. Divided by R two here in case the columns constrained and there are one and two are the distances from each other&#x27;s to the center off that square, since both charges are equidistant so we can write our one equals toe to equals law. No sitting this swelling into the equation and then taking the carry. What is bad? It&#x27;s common. We can write this question as you recourse to caddy wanted by, uh, into Q one plus you&#x27;ll do. From here we can write to one equals two minus over 22 equals two minus of Kuan Onda sitting really off to one, which is a capital to weaken right. The value for two to us Q two equals toe minus Captain Cure So this is the answer. The first part of the problem. In part B of this problem, we have to talk about the natural for electric potential point there ask you one his nature to this point as compared to the q two and it has posted child. So the elected potentially point there will be positive. In the last part of this problem, we have to talk about the nature off the field at point B here to do is nearer to the charge to one so and they had to either get you So we can say that this field at point B should be Thank you.

Ze-Han Lee · Answer

So in this problem, we have a four charges. Ah, positive. Negative. Negative in positive. Right. So this is a positive Q. There&#x27;s a negative que negative Q and a positive Q. So according to the problem, we know that the net force acting on the positive Q zero in part I want to find out relation off the small cue in the cab a cue. Okay. Ah, If we do the force and the nice is on this charge, you see that we have the attractive force toward this direction an attractive force or taught toward this direction and the repulsive force towards this direction. And ah, it is incredibly, um, in the, uh, in the three forces. So the fool&#x27;s induced by the two attractive force Has magnitude over skirt a while or four, perhaps on a lot times Q Q Over. So suppose the separation of Themis ah dee over de squid and the combination of these two forces will be toward this direction. Hey, and this is the combined force and the magnitude of its force equal this one time score too. Okay, so, uh, because because this charges in equilibrium, So the magnitude off this force will be equal to the repulsive force. Right. So this sequel Well, we&#x27;re four pi. Absolute, not times. Q squared over. So the separation beaten to pause it Charges of square two times D All right, so squid. So we have this equation now, right? So you can solve this equation attended to the small Q equal. Uh, negative, Q over. I&#x27;m sorry. Smokey is positive here. There&#x27;s a positive because we list we already moved this part native side in front of smoke. You Okay, so is Kyu over a squared to square two. Okay. And the in part, be willing to know that the net force acting on negative que eyes is you&#x27;re not. So I would tell you that it&#x27;s not zero, because ah, so again, we have this model, Ray. So this is a Q negative que negative here on the Q. So the force and therefore is acting. We have ah attractive force toward this direction, and we have a repulsive force toward this direction. Right? So the magnitude of this attractive forces while over for pie have so not times Q Q over the squid, right? And the combined force of this too it&#x27;s toward this direction, and the magnitude of this force is they call this one time score, too. And the repulsive force has expression. What over for pie? Absolutely not. Times que squid over square two Oscar, two times thes quit, right? Remember that to smoke you only equal Q over to score two. So we applauding the expression of this monk, you in terms of the counter. Q. You&#x27;re seeing that this term is not equal to this term. All right, so they did not equal each other. So therefore sacked in the smoky is not zero in Parsi. Want to know the electro field? I was sent on the square right here. Oh, it&#x27;s easy because the electric fuel induced by the two positive charges a zero right, just according to symmetry, because the electrically induced a marked by the by this wine is pointing to this direction and induced by this one&#x27;s pointing it, pointing to this direction right, So these two factors would cancel each other, and Elektra feud, induced by this one, is pointing to this direction. They&#x27;d atrophy induced by this one&#x27;s pointing to in this direction, and they also can&#x27;t reach out there. So the net electric force at the Centre zero okay,

Ben Nicholson · Answer

16.16. So we have an equilateral triangle, uh, lists equal charges positioned around its center. So we want to show first that the electric field in the center is equal to zero. Then we want to find an expression for the potential with the center of the triangle. Then we want to explain why the potential is not zero, but the electric field is. So the reason that the electric field zero here is because of the symmetry of of this, um, set up at the the center point, we&#x27;re going to have an electric field directly downward an electric field like this. That&#x27;s, uh, and declined at 30 degrees and another one like this that&#x27;s also inclined at 30 degrees from the horizontal. So the x component of the electric field there if we say these all have a magnitude of e one or something. So for X, we have just these two. So we&#x27;re gonna have e one co sign of 30 degrees minus because this isn&#x27;t the negative extraction. He won co sign of 30 degrees. And so obviously those cancel out than in the wider action we&#x27;re going to have, um, two times e one times sign of 30 degrees, just the white components of these two. And then from that we&#x27;re going to subtract anyone because this is pointing straight down. And, you know, the sign of 30 degrees is 1/2 and so it was also canceled. So no electric field at the center now to find the potential. This is just the sum of the potentials from each one of these at this distance away. And now this only depends on the distance away and not on the direction of anything. Some over I take you, I over our I. But all of the cues and distances are the same. And so this is going to be three. Take you over a now The reason for this being non zero here, first of all, these don&#x27;t contradict each other because recalled it, the electric field is given by the derivative or grady in of the potential. So the potential is going to have a maximum or a minimum here, so the radiant will still be zero and the electric field will be zero. But this has to be non zero. If we say the potential is zero out an infinity because We have to do some amount of work to bring a test charge to this location, and the potential tells us how much work a test charge has to have done on it to bring it to a particular location. So you&#x27;ve been in a region or a point where the electric field zero. If it still took some work to get there from infinitely far away, the potential is going to be non zero.

Nicholas Majtenyi · Answer

question 50 asks state that the electric field lines threatening the three treasures shown, indeed, drawing that I tried to make here. Um, the Centre Charge Q two is native 22 0.8 Micro columns What are the signs of Q one and Q three? Find Q one and Q three. This one just tried to rescue on. One of the Middle is cute, too, and I&#x27;m on the right. Is Q three. So I told the magnitude of charitable and signing us of Q two 20.8 Micro cool rooms. The first all primary. One of the signs of Q one. Q. Three. Well, we see the electric grid lines are leaving you to the point charges, so that means both Q one. Q one and Q 23 53 are positive again because electrocuted lines leave the charge, meaning that it is a positive charge. Barbie is find Q one. So you know, that&#x27;s, um, looking at this. The sign of Q on your field lines, the number of electric field lines proportional, many see diagrams. I guess the no SE number of e field lines is proportional to the electric field itself. For the challenge. I should say nothing. Not the Are you feeling self? Which in the messages, actually. But to the charge Presence seven was for cute to, um, I believe I matched it well within the book. I mean, the book is a much more accurate, but it should be balanced on both sides. But as we see, there&#x27;s 1234588 from each sides of 16 electric field lines entering Q two. That means there&#x27;s eight killed lines, leaving both Q one and Q three. So since the electric field lines for Q one equals 1/2 the electric field lines entering cute, too. That means, by that logic, that you the charge of Q one, has to be half that of Charge two, meaning that it is 11.4 micro Coombs. And again, that&#x27;s positive. And C because it&#x27;s exactly the same, Askey one. By that same logic, you would find that the electric start the electric charge that&#x27;s right of Q three is also positive, and it is also 11.4 micro cool. It&#x27;s exactly half of the I feel I was exactly half of the charge of cute, too

Katie Mcalpine · Answer

Okay, so in this question, our goal is to find the electric field at the right lower corner. So let&#x27;s go ahead and draw. The charge is minus two Que and the top left, and then cues, right. Some minus two Q Que que distance is A. This distance is a And then here&#x27;s the bottom right corner. So just checking on my drawings. Okay, um, let&#x27;s draw electricity weapons that the electric fields from each component. So the minus two Q is gonna be towards the minus two. Q. Um, in this direction, the plus q is gonna push this way, and then the plus Q about top is gonna create a field that way. I&#x27;m not quite sure of the magnitudes there. Probably more similar in magnitude than I drew them. Um, so let&#x27;s go ahead and label these. So this one is cake you over a squared, right? Because this is the distance a, um and it&#x27;s cake. You, uh, no. As columns logic taste, this one&#x27;s also cake you over a squared. Now, this factor is, um, que times to Q. And then we want to divide by the distance between these two square so that distance is the square root of two times A. So that&#x27;s actually two screwed of two times a, um, are starting to a squared because that&#x27;s the same things. A squirt of to a squared. So that means it&#x27;s actually the same magnitude is thes other, um, these other vectors, So they&#x27;re all through the same magnitude, but this one&#x27;s out of 45 degree angle. So if we break this up into its components than it has a horizontal component in a vertical component, each component is, um, is the same cause. This angle is 45 degrees on because it&#x27;s a 45 45 90 you&#x27;re just gonna take the triangle and cut it by square root of two resorted take the value and cut it by the squared of to write for a high for the high pot. News of ah sauce really is. It&#x27;s a in squared of to, uh, a so this is always one over square to to a from this. So that&#x27;s the vertical, and that&#x27;s the same thing as a horizontal. And so now if we want to add both of them up now, now we went addle the vectors up so the, um So let&#x27;s kind create a coordinate system. This is the X axis, is why this is positive. And then, of course, this isn&#x27;t I I had to long destruction and J hats along this direction so we can say is equal to Let&#x27;s do that. I hot first. So, um and the positive I have we have cake you over a squared on then and the negative I how we have cake you over a squared, squirted to and the j hot we have, um it&#x27;s actually the same thing. Oh, almost the same thing, the negative of it. Right, Because now we have a positive que que, over a squared square, too. And we want to subtract off que que over a squared so we can take out a cake. You basically out of the whole thing? And then, um oh, actually, we could just there going all have the same coefficient except one will be negative. So what&#x27;s figure out what this is? So I mean, you can put them under, um, the same denominator. So they will have a square root of a squared on the bottom, sort of to a square. But then this one needs toe have us be multiplied by the square root of two. So then we&#x27;ll have, um, que que times the square root of two minus one. And this one is the same thing except for us, the opposite direction. So then we just have my hat minus jihad. So it&#x27;s kind of hard to watch somebody else do address. So I encourage you to just do this one on your own. My am instructions didn&#x27;t make sense. Um, yeah, you can probably algebraic Lee manipulate this to get different, um, answers, like with describe it of to.

Problem

Graph cannot copy The figure above shows two poi…

Problem 3 Easy Difficulty

The figure below shows three point charges, all positive. If the net electric force on the center charge is zero, what is the value of $y / x ?$
Graph cannot copy
(A) $\frac{4}{9}$
(B) $\sqrt{\frac{2}{3}}$
(C) $\sqrt{\frac{3}{2}}$
(D) $\frac{3}{2}$

Answer

Related Courses

Cracking The AP Physics 1 Exam

Related Topics

Discussion

Top Educators

Recommended Videos

Watch More Solved Questions in Chapter 10

Video Transcript

Robert Franek

Cracking The AP Physics 1 Exam

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

Cracking The AP Physics 1 Exam

Robert FranekCracking The AP Physics 1 Exam

Robert Franek

Cracking The AP Physics 1 Exam