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Four point charges of magnitude 6.00 LC and are at the corners of a square 2.00 m on each side. Two of the charges are positive, and two are negative: What is the e...

Question

Four point charges of magnitude 6.00 LC and are at the corners of a square 2.00 m on each side. Two of the charges are positive, and two are negative: What is the electric potential at the center of this square, relative to infinity, due to these charges? (k = 1/4n80 8.99 x 109 N. m2/c2)The potential at the midpoint of a square is 3.0 V when a point charge of +Q is located at one of the corners of the square (the other 3 corners are empty). What is the potential at the center when each of the o

Four point charges of magnitude 6.00 LC and are at the corners of a square 2.00 m on each side. Two of the charges are positive, and two are negative: What is the electric potential at the center of this square, relative to infinity, due to these charges? (k = 1/4n80 8.99 x 109 N. m2/c2) The potential at the midpoint of a square is 3.0 V when a point charge of +Q is located at one of the corners of the square (the other 3 corners are empty). What is the potential at the center when each of the other corners also contains a point = charge of +Q?



Answers

Point charges $q_1 = +$2.00 $\mu$C and $q_2 = -$2.00 $\mu$C are placed at adjacent corners of a square for which the length of each side is 3.00 cm. Point $a$ is at the center of the square, and point $b$ is at the empty corner closest to $q_2$ . Take the electric potential to be zero at a distance far from both charges. (a) What is the electric potential at point a due to $q_1$ and $q_2$? (b) What is the electric potential at point $b$? (c) A point charge $q_3 = -$5.00 $\mu$C moves from point $a$ to point $b$. How much work is done on $q_3$ by the electric forces exerted by $q_1$ and $q_2$? Is this work positive or negative?

In this question, each charge of magnitude Q equals to 1.5 local. Um and when minus Q. Charts are placed at the corner of the square of side, L equals to the way that is equal to five point 40 centimeters. And point P is in this space located above. And the diagram can be drawn like this. Ok, so this will be the diagram for this situation where these are the three point charges and this is the next negative charges. Negative charge. Okay. And the point P is situated at this point. Okay. Zero comma zero comma C. Okay. And this distance is the R. Which is the distance between point P and any child? Cute. Okay. This any charges Q. So this will be the distance are so from the geometry we can write that small are this will be equals two under root of L by two. Holy square plus L by two. Holy square plus C square. So from here we get our equals two and the root of elsewhere by two plus C square. Okay so the electric potential at this point will be given by pee wee. That is equals two. Okay thank you. The where we are for this charge and discharge and this charge we can write this will be multiplied by three times. Okay? And for this charge we can take it into negative so minus K. Cuba. Are okay so it comes out to be two K cuba. Are now we can substitute this value of our here so we will get that potential at point P. So we come out to be cake you develop our which is elsewhere by two plus C. Square and understood. Okay so now we can substitute with the values so we get potentially equals two K. Which is 9 to 10 to the power nine. And this is to and to clarify Q which is 1.50 multiplied by 10 to the power minus nine column, develop a under root of el, which is 5.54 year centimeters. So that is zero point zero point 050 540 meter divided by two. So Holy square plus C. Which is equals to see which is 4.10 centimeters of 0.410 m. Holy square. Okay, so from here after solving, we get potentially equals two for eight. Even World. Okay, so this become the answer for this question. Okay.

Abortion. It was stated that there is this Where of suicide? Two centimeter with 29 Dustin Microphone charges, the adjustment corners of the of the square and two minus 3.0 microphone charges at the centre car at the other corners. So as in distributors, where decide a close to two cent immature and he's just sent corridors charges Q 19 microphone. And it's also killed nine micro production and these two sides. The charges are the charges are minus three microphone minus three Microphone. And this this is also minus three microeconomic issues secured. Three. Yeah, so I have to find out the electric field at the center from the each side. The distance of the center is the two and you're ready to, which is one way to state immature. So we shouldn't go into mathematics or calculation there, just by simply very simplified from the case. From the intuition we know from these charges are saying. So this will be the electric field for killing. Just at this point is to our Q two and Q two, and for the electric field at the center for Q two is equal and opposite. So then they filled up for this, too, which is zero a Q one, Q two. That it goes with your synthesis, Uh, for Q three Dielectric Resort. This is this side. And for this also same charged electrically would be on the other side for for this to church, then that electric. It will also be zero sorry three and Q four that that also zero so that that electric field is always do at the center that shit.

And this question were given that identical charges Q. The magnitude is given Are placed at opposite corners of the square. There is a length of eight cm. So we have a square and let's talk about its pictorial representation. So we have a square over here and these are the words is A. B. C. And D. Point is one of the empty corners. So this is empty and point B is at the center of the square. So let me just redo this is our anti corner and B is at the center of the square and the charge of prison opposite corners of the square. So this is charged you and this is charged you and this one is going to be all right. Uh So what we have to find out is a charge of Cunard. A charge of Cunard is placed at the point and moves along the diagonal of the square be so where the magnitude of the net electric force on cue, not when it is appointed. So there's another charge Q. Not which is at A. So we have to find the net uh electric force or human, so that's going to be as that's gonna be because of this Q. And this Q. These two cues. And since Q is positive and human orders negative, the force is going to be attractive in nature. So brisk force, let's say is represented by efforts over here and the magnitude would be seen for even this force since they are symmetrical. So there is F over here as well. So, since these two angles are at 90° to the result and force the result and force F net has got to be f route or route to have because they are at 90° with respect to each other. So this is a spot vector addition property. Now the value of F is going to be care times Q times Q. Not over our square. Where r is the length of the side which is eight centimeters. So we're going to write 0.8 old square meters. So let's substitute the values here. We have the value of ks nine times 10, raised to nine. The we have the value of cuba's five times two and raised to minus six. The value of Q not as magnitude is three times 10 raised to minus six Over 0.08 square, grab my calculator over here and do this calculation to this work. So that's going to be equal to nine. Route two times five times three, 102 times five times three which is, and this should be divided by a 30.8 square. So that's coming as 29831.6733 times 10, raised to uh a minus 3/1, 23. So this is going to be equal to 29.83 newtons. This is the net value of the force which acts on the Q. Not at point. Uh Now it says that if sketch the placement of the charges so that we have already done And the direction of the net force, the direction of the net force is going to be over here and this will be at an angle of 45° because they are at 90°. Uh And uh then it is asking that, what is the magnitude of the net electric force when it is RB. Now, Cunard has moved to the point, be secured orders over here. So what is the net force? And that force is definitely gonna be zero because this is attractive over here. This is attractive over here. So there are two forces which are equally in opposite to each other, that's definitely going to be cancelled out. So we are, we will say that the F net and B. And got to be is going to be zero. The next one is, we talk about how much work does the electric force due on Cunard uh during its motion from A to B. So that we have to find uh the network done on the electric by the electric force in the motion. So we're gonna use the formula. Now, the work done is given by a few times the change in the potential. So what we're gonna do is we're seeing are the well done. The walk and done is going to be cute times the potential at B minus the potential arctic and Q. Is definitely cute not because you're not a small. So it's Cunard. Now what is the potential at B. At B. Or a. That's going to be because of these two charges. So uh since the potential is a scalar quantity we can just add. So at B. That's gonna be Q. Over. Uh you over for by absent and are So let's let's make a figure over here at B. Let's find or due to just one charge. So we've got to find this distance which is half the diagonal. So for half the diagnosed, we know that the diagonal is if the length is uh if the length is given as Eight cm. So diagnose gonna be uh 8 0.08 route to and this length is going to be half the diagnosed. That's gonna be 0.08 route over. And this is what we're gonna use over here. So because of one charge for the two charges, they're going to be multiplied by two. So that's gonna be two times KQ Over this distance are so this distance are is nothing but 0.08 or minus the potential. It is. So the potential today is again going to be two times the potential due to one. That will be KQ over R where R. S. Um Where are these businesses? Because the queue is over here. So the R. is going to be the length of the side, only 0.0. So let's substitute the values over here and get get the answer. So we have KQ has taken out so we have cake. You do not uh In fact two K. Q. Q. Not. Uh Then we have route to over 0.80 point 08 minus one or 0.08. Let's put the values of the queue is five and this is minus three. So that's gonna be a minus two times nine times 10. Raised to nine times five times three times generates two minus six and minus six. Will become minus. Well, because this was given in micro problem And this is route 2 -1 over 0.08. So the work that is actually coming in negative and we'll find its value. Let me grab my calculator over here. So we have room to minus one over 10.8 Times two times 9 times five times 3. So this is coming as it should be divided by 10 raised to my industry. So that's coming as the world is coming as negative, 1.4 jewels of corporate similar places. A negative 1.4 jewels is the required well done after pulled a similar places and uh the world and positive or negatives are definitely that's negative. And when it goes from A to B disk union moves to higher potential, lower potential. So definitely when it is going towards B, it is moving to a lower potential. That's because we can clearly see that since it's moving uh is moving to a higher potential because we can see that this is the potential our beef, This is the potential Art B and uh not including the two. Yes. So we can include the two as well. So this is the position, this is the value at B and this is the value are. So clearly we can see that when we simplify it, We get we get this route to -1 or 0.0, which is a positive number. So it means that we are B as greater than the we at A. So it means that we are moving towards a region of the higher potential because we b minus we is uh as positive. But if it's because of the charge Cunard, which is negative, that well done is coming as negative. So we're going to say that we're here, we can write that it is moving to a higher potential. Thank you.


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