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Two pcint charges; 91 22.74* 10-6 C and '92 = +I(4.11 xIOI3Je] are located on the y axis s0 that 91 IS directly above 42. (Note [s the fundamental e ectric cha...

Question

Two pcint charges; 91 22.74* 10-6 C and '92 = +I(4.11 xIOI3Je] are located on the y axis s0 that 91 IS directly above 42. (Note [s the fundamental e ectric charge, and we are only cansidering the X-Y plane:) The coordinates of 92 Is (0.00, -12.8 cm): The two charges are 38.2 cm apart. Determine the coordinates of the location where the net electric field due to q1 and 42 Is zero. Give your ans-ver [ the form "(a.bc m, +/-d,ef m)".Answer;

Two pcint charges; 91 22.74* 10-6 C and '92 = +I(4.11 xIOI3Je] are located on the y axis s0 that 91 IS directly above 42. (Note [s the fundamental e ectric charge, and we are only cansidering the X-Y plane:) The coordinates of 92 Is (0.00, -12.8 cm): The two charges are 38.2 cm apart. Determine the coordinates of the location where the net electric field due to q1 and 42 Is zero. Give your ans-ver [ the form "(a.bc m, +/-d,ef m)". Answer;



Answers

Two point charges lie on the $x$ -axis: $0.25 \mu \mathrm{C}$ at $x=0.25 \mathrm{~m}$ and $0.16 \mu \mathrm{C}$ at $x=0.75 \mathrm{~m} .$ Find the place(s) where the electric field is zero.

So here let's say we have two charges and these two charges are opposed in nature and they are having same magnitude. So let us say one of the charges Q. And another will be minus Q. And these are placed at the coordinates, let's say zero E. And zero minus C. So they are place like zero and 0- at these two points. Yeah, So we have to figure out, let us say cute charges placed here and minus Q. Is placed here. So we need to figure out what will be the net electric feet at any point D. Zero. Yeah. So the zero will be, it can be here or it can be anywhere to the left. We are not given whether these positive or negative. So let us take this. So now the electric field due to this charge will be in this direction and due to this charge also it will be in this direction. So the magnitude will be safe because the charges are seem. So let us find one charge one electric field. Let's find, let's say we will figure out this electric field so that will be due to the point church key cuba are square. So Kay into charge over our square. So are is the separation. So we have the idea that this is A and this is D. So we use pythagoras student to get this hyper luminous of this right angle triangle. And that will be route a square D. Square whole square of this. So this will be cuba. Yes square please. The square. But this electric feed now this electric field can be projected along X. Direction and Y direction. So let's say it's projection along axis mm cost peter whereby this angle theta. So for this also by symmetry, this will be twitter. So along this we will get to ecowas theater and their vertical components will cancel. So the net electric feed at this point D zero which is given to us. So it will be two times E. Will be K Cuba A squared plus B squared times crossed pita and cost theatre. If we observe here, just apply simple geometry. This is theater. So this will be to buy particularly apposite angles here and costs can be obtained from this right angle triangle. It will be D. Over this hyper newsline. So we get the net electric field as to take you by a square place. De square times B. Bye. The hypothesis again that is the root of a square place. De square. So combining this we get the net electric field and that is to take you deep by a scratch place de scrapped Raise to three x 2. And here the value of K is one by four pi epsilon. Not supporting that, we get the net electric field as two two KQD. So instead of KV right it has 457. Not so too into QD by for by absolutely not times a squared plus B squared raise to three by two. And this electric field will be along the positive X axis. So we can see Icap. And the next thing that we need to figure out here is the same thing we need to repeat for two equal negative charges. So let us say we had the similar configuration and one negative charges here, another negative charges here. So they are placed at zero a and zero minus. So we want to find out the net field at this point D0. So again, due to this electric field will be in this direction and due to this it will be in this direction. So magnitude of electric field which we calculated, that will be same. So let us take This value of electric field in equation one. So this IV will be cake you buy. Yes, scripless descript and here again by symmetry this is theater. So here also it will be to Sonett electric field will be in this direction because this projection gives us E costa and this also gives us ecos theater. So it will be to Ecowas theater. So again we use to eat cost data to get the net electric field. So this is to be cost data. It goes to this. So two times this was E and costly to again in the strangle picket. This as be over This by three x 2. So this is the electric field along negative max direction. So here we have certain conditions that electric field will be equal to. Let us say this magnitude is E E dash, So -1 I kept if these positive and it will be plus E dash I kept if these negative. Similarly, we have the rule over here as well. We were saying that electric field was in the right direction. So let us say this value is a dash. So the net electric field will be E dash I kept if he is positive and minus E dash. Hi cap. If these negative. And now we need to plot the grass for these fields as a function of B. So let us take the electric field, the net electric field whatever we have got. So let's say we want to plot for this. So electric field as a function of the so fast here we will have it has X. And so let's say this represents not X. Deep. This represents me and we need to find out the electric field. So if D. Is positive, that means electric field as we go away in the second situation went to equal negative charges, were there? So electric field came out to be negative if the is positive and this electric field yes, going to be a cup. So electric field will decrease if D. Is positive and it will decrease to zero. So it will be like this and it will increase if we go to the negative end, this will be for the second case. For the first case we can see electric field will be negative if these negative and it will again not decrease here because you see here, if we want to find out the net electric field at this point, then due to this charge, it will be in this direction due to this charge, it will be in this direction. So overall the electric field is increasing. Yeah, so our graph is going to be and increasing curve, which will be like this and here you do symmetry. It will be like this.

Two charges Cuban equals 2 -3.0 my curriculum which is located at minus 0.50 m comma zero. And another child skill to equals two minus 4.0 micro column. Which is located at 5.0 point 50 m comma zero. Okay, so let us draw these two charges on the axis. This is our X axis. Because both the charges are located on the xx is say this is our origin. Okay, this is our reason. So no, this point is a reason and Cuban is placed at this minus 0.50 comma zero. And the Q two is placed here. So which is at zero point uh 0.50 0.50 comma zero. Okay so this is our child Cuban and this is our charge cuba. And this is our origin. Zero comma zero. Okay. Now let us suppose a point which is situated at a distance small are from here. Okay, so let us suppose this is a point P we're not electric field is zero. Okay, so this total distance will be one m because both are 0.5 m from the reason. Okay, so the net electric field at this point we will be Cuban due to the charge Cuban, this will be Cuban by and these restraints which will be one minus are okay these restraints will be one minus are so one minus r holy spare and this will be K you to buy our square. Okay, so as not electric field is to be zero here so even the equals to eat. So substituting values he get Cuban by one minus our holy square. This will be equals to take you to buy one. My are square. So now substituting value of Cuban and Q two. So Cuban is three magnitude And they were by even minus are fully spare. This will be equals to four divided by our square. Okay, so from here after solving we get our equals two to buy under route seven Ex and this is equal to 0.256. Meet. Okay. uh 0.756 0.756 m. So now we can see that this distance is 0.756 m from here. And from here to here the distance is 0.50. So at this point will shift towards the left of the origin. Somewhere here. Okay, this point will be here so we can say that for the part of the question. The point lies on the left of the Parisian. Left of the Parisian. Okay, so this point is line at left of the politics. The first option is correct. Okay now for the part of the of the problem, the distance from the X axis is this re stains from the X axis. This saves X. So this is equal to x equals to this total distance is 0.756. And this from here to here that extends 0.50. So 0.50 Meet. Okay. So as this point is towards the left so we can take minus sign for this question this distance so actually equals 2 -0.256 m. Okay, So at this distance the electrical is G. Okay? So this is the answer for the party and this is the answer for the part. Okay?

This problem we have given a 23 6 microbial um point charge 23 6 micro column friend charge lies at the origin. So this is suppose X axis. And this is the point where Q charges placed. We have to find the electric field at distance. 0.95 comma zero. So this is the 1st 00.0 comma 0.95 comma zero. So we have to find electric field at this point. So electric field direction will be towards positive X. And we can find the magnitude. It is equal to K. Q by X. Square scale is nine into 10. To the power nine Qs 23 6 into 10. To the power -6. Buy XS Square x 0.95 square. So this electric field, will we call to 19- 24 Hour 9? Not to play with 23 6 entered into the power -6, divided by 0.95 sq. It is a cool do Yeah. 2.35 in 210 to the power five newton for column. This is the electric field in each direction. Now we have to find directed field at point which is placed I suppose this is xx by accident, this is X axis. So here this point is placed somebody here and this is the charge. We have designed the electric feed. So this will be the direction of electric heat And the coordinator. This is 1.25, Coma, 0.75. So there will be two components, X components E X and Y components supposedly by. So we will find E X will be called a K Q by X square where X is 1.25, which is equal to 1.359 Into 10. To the power five newton curricula. And if I is equal to K Q by square, so we will put value Y, which is zero point 75. So it is equal to, yeah. Mhm. 3.77 6- 10 to about five Newton Markkula. So the electric field at this point, we can write in the component form. It is a call to 1.359 into 10. To the power five I kept plus 3.776 into 10. to the power five Jacob. This is the electric field. Mhm. At point 1.25 comma 0.75. This is the answer for partly and for part a electric hell is this? Thank you.

I have given f there are right. You too. And do tree their electric tree. Yeah. Mm. Cancer and E. Would we, Joe AC access card. 2.3 m in the region. So Yeah, Cuban. The evil cancer to them. Yeah. Mhm. Mm. Left off 13 m. Very slightly, slightly larger. Okay. It will cancel them. Mhm. Mhm. Even this is the answer of, you know, be part. Yeah. Uh huh. Mhm Pipeline problems. Lab in battle from Total Electric Treaty. He might escape you upon Access Square. I kept kill upon X minus point to I kept so it can make a difference. Yeah. Sorry. Press. He came upon x minus. Yeah. Mhm. Mhm. Okay, yeah. Mhm. So from here, if it is to me zero so you can write minus one upon exit square. Mhm. What is square minus? Yeah, Mhm. But let's on solving it. You will get X is called 2.297 m. That so? Thanks for about


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