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Chapter 24, Problem 063HTwo metal spheres each of radius 3_ Cn , have Center-to Center separation of 2,3 Sphore hiaz charge of /1, * 10-3 C; sphere has J charge of ...

Question

Chapter 24, Problem 063HTwo metal spheres each of radius 3_ Cn , have Center-to Center separation of 2,3 Sphore hiaz charge of /1, * 10-3 C; sphere has J charge of 3,8 * 10-8 C; Assume Ihat the separation Is large enough tor us t0 assume that the chargeon cach sphere uniforitly distributed (the spheres do not affec: each othe ) Witn V 0 atirtinity; Calculate volts (a} the potential atthe point halfway between their centers and the potental on the sutace cf () sphere (c) sphere(a} NumberUrits(b)

Chapter 24, Problem 063 HTwo metal spheres each of radius 3_ Cn , have Center-to Center separation of 2,3 Sphore hiaz charge of /1, * 10-3 C; sphere has J charge of 3,8 * 10-8 C; Assume Ihat the separation Is large enough tor us t0 assume that the chargeon cach sphere uniforitly distributed (the spheres do not affec: each othe ) Witn V 0 atirtinity; Calculate volts (a} the potential atthe point halfway between their centers and the potental on the sutace cf () sphere (c) sphere (a} Number Urits (b) Number Units (c} Number Units Click it You would like to Show Work for this question: Qrenshow Works



Answers

Two metal spheres, each of radius $3.0 \mathrm{~cm}$, have a center-to-center separation of $2.0 \mathrm{~m} .$ Sphere 1 has charge $+1.0 \times$ $10^{-8} \mathrm{C}$; sphere 2 has charge $-3.0 \times 10^{-8} \mathrm{C}$. Assume that the separation is large enough for us to say that the charge on each sphere is uniformly distributed (the spheres do not affect each other). With $V=0$ at infinity, calculate (a) the potential at the point halfway between the centers and the potential on the surface of (b) sphere 1 and $(\mathrm{c})$ sphere $2 .$

Okay. So basically we have even over here that H. L. Uh two models for each of these trees in the middle and have a center of 160 centimeters right? So let's say this is the atmosphere. Okay. And the central, central person believing them, the distance from central center that is too bitter and it's already stationed in each other and teaching the dread. And One more thing that charges money. It's one in regional development, uh, other reasons. So one internal developments wait too long and over here. The Ministry of Development eight cooler. Okay, so this is the charges under there. So I assume that that situation is large enough obviously to, you know and permit, consider the time on the field. Is any formulas to reduce the discharge is not if you keep this one and this one is not a family run away. And so what we need to do is that with this, so calculate the potential half between them and the potential that each of us in the first part potentially have between them will be nothing but the distance from the center to this one. They say that is one something that potentially do nothing but Cuban upon our one plus kids you to upon our book. Sochi is nothing but 900 09 into cuba needs 10 to develop minus eight on our on our own is one region because half of them so one And minus about it because they're 1920 out of nine into this security 300 to organise side obviously are now these changes one with them because they decided negative. So this comes out to be when we do calculate this comfort to be members of 6:30 world. Exactly. Now in the next part you want to find a potential at each of the six year surface for the first one. But that one will do nothing but KQ one upon our one and plus KQ two upon the distance from the center to the surface with regard to the distance from the their center to the their center is two. And the radio systems and environments. That means from the center to the service will be two minutes of your appoint trees. Okay, so our rural distance went so far. So that will be nothing but nine into conductive our of nine into Cuban Cuban 8124 of minus side upon. I want is to send emails that were still in new york minus two and plus the already minus because this is the negative chance. Mhm. Crazy About into a ball average at this age two m 2 minutes of 300 development store. Okay, so this potential This potential comes out to 26 343 26 3 4.3 World. Okay so this is the principal the first success in the peninsula. The sergeant success. And then we can take you to upon our two plus Cuban upon ar minus so far. Okay. So that we'll do 900 negative because negative so 9 to 3 in different developments. It upon our one is 113 $700 managed to And plus 19 to 24 months, nine into one in 20 rounds of genocide upon Distance is also two minutes of continued from the uh -2. So this is a so called comes out to be minus of 23954 World 123954.4 bold. So this will be the hour and says okay.

In this question, we have to metal spheres mm and they are, to me, the part Each of them has a radius of three cm. So it's one and 2 you want is um, the one is can an okay, you too is negative 30. Okay, so, um, so we want to find electric potential uh, due to the two spheres at different points. Okay. So, um, the first point is the midway between the two charges and then the second point is on the surface of sphere one. And and lastly on the survey, the atmosphere to Okay, so this is part of A and this is part B. Okay, This is Patsy. Okay. So to solve this problem, no, Dad, the electric potential electric potential is the sun of the contributions. Yeah. After individuals fields. Okay. So in part A pay at the midpoint. Okay. So, uh, at the meeting point We have e goes to one Class B two. Okay. For each V is uh Q one divided by four pi s or not? He and then Q. Two by four pi. So not the case in this case the distance are the same. So I'm just liberate. S. D. N. P. R. D. Is one m. Okay. And so if you calculate this um you have 8.99 times 10 to the night because they have a common term. Thank you. Want to ask you to Thank you. one is and then a colon. And then my nurse uh latino column. Okay. And then divide by one. Okay so you can copy the v. to be uh negative 1.8 times 10 to the two words. Okay so this is the answer for pain even in bobby. Okay. You want to calculate to Naruing at the surface of still one mm. So. Okay so we want a sequel to, I want to work for pie Exxon on. Mhm. I ask you one you can buy our plus The two there are buying D -R. Okay. Yeah d. is two m. Yeah. Yeah so maybe in pay I will put the over to the to just to make it consistent. So this is two m. Okay so You can put in the numbers 8.99 times 10 to the nine. Okay so the reason why there is a D -1 is that so um he says E. And then this is the are so um yeah so she uh the effective distance becomes the minus are okay. He's opening all the numbers. Okay and you calculate that you get 2.9 times 10 to the three words mm. Next patty patty is a similar approach. It's B. K. So at the surface of sphere to okay so we two is equal to 1/4 pi perhaps or not times Q one over B minus R. Plus. You too. Bye bye. Are okay between the numbers, Right? So calculate this, you get -8.9 times 10 to the three votes. Yeah, So if it's the answer for Patsy and that's all for this question.

So the electric potential can be defined as the work done by some external force Mobile charge from the reference point to a specific point in electric field to the equation for the electric people can be defined by this following expression so easy for two cakes You over to me Square. So here case electrostatic constant circle constantly was charged R is the distance between the point charge to the inner charge to the expression for the electric potential. Is this once again such the interval from So if you move on to part nails do that purse So part a The electric potential from infinity to the point C is equal to the interval from infinity to see and e v er so if you substitute for E, we're gonna get that equal to negative Infinity to point c take you r squared and integrated with respect and er so if you integrate that we're going to get that. The final answer is que que oversea So therefore, the electric potential ft on the surface of the hollow sphere is this So now if you move on to part B electric potential at the surface of the solid fear at a is the A equal to negative, uh, from infinity to see er minus see from the point c to be. And then again, er we're going to get rid of these two lives here, intruding once again they're tossing minus the potential from it from betray E e r. So So if you replace the values since you already calculated this in the previous stuff, it's just take you oversee and we know that potential from D. C zero. So it's just a zero, and then the final long it's just get you So she meaning to integrate this So take you be true a, uh d r her. So if he into it that and we simplify with the foot with the expression next to it, That way we can factory kick you since it they're both and it's gonna be one oversee minus one over B four spot over a. She put in the country on integrated. So therefore the electric potential at the surface off the soldiers were is equal to this. So if you move on to part C, sorry, this was part C. Yeah. So, for part second, this is part seeing Let's go ahead of you. This is part C and part be essential at the inner surface of the host here, FB is actually equal to this. This as well. Now, if you want to party potential at the inner surface of the sorry, So the potential the electric potential inside the sphere is equal to the potential on the surface. And therefore the potential at the center of the solid sphere can be represented by the following. Sylvie a hold on my mouth just disconnected if you could give me a second to connect it back. Sorry for the delay, but my mom's just disconnected in the middle of it. And there we go. We're back on track. So be a is equal to therefore, the potential inside the sphere is equal to the potential on the surface. So the potential on the inside the sphere is just equal to the same thing because there are three potential surfaces. So I only I don't think I need to write that again. But I was just strong hired to make sure that you're clear and that's it for this guy.

Oh hello. So for the twist to this fear the two states that are connected. Uh huh. The field is given by one of the four by you. Note Q. What About Our School 1? And the potential as all over 45 absolute mint Q. And a mm. Without charge. Q. Is the some of the charges Q. On. Thank you too. And a voltage we'll get the same 42 charged. Yes. But it's just the yeah. Now the fact that the voltage on the two faces equal leads to This conclusion that Cakey one over Iran equals K. Q. To R. Two. So Q. one or 2 I think Rose Q. Two. All right. But we can write queue to us. Capital cumin is Cuban. So this is a mass. Capital cumin is Cuban. Everyone. So remember that Q. two equals Q minus Cuban. That is what we have put here. So we can then make substitutions for he wanted you to Q. On any clothes. I run over uh R. one plus R. two. Human. And cute too echoes. Q. R. Are two of a Byron plus R. two. That is in trying to make you want to take you to the subject in this expression. Mhm. Mhm. All right. Let's give the some of the queue here. You know in see we had to write expressions for Mhm. Think shop to be one. It was one of the 45. Actually, I'm not Q. One over everyone. And that becomes cute over. Bye. Absolutely not. uh I one plus uh to that is substituting for Cuban from here. This woman is Cuban and that is if you want are we too equals one of our four By absolutely not a clue to give me a substitute for Q two And I'll give us key one. Uh huh probe. I absolutely not Iran plus our cube. And you can see that in the end v. two. It grows. Do you want Okay. 3 3 calls. We want our sweet uh stated here when he calls me too. Be one expressions for the few. You only called R. One, Jericho's Cuban. What are absolutely not of Argon? Yeah, I want last hour two. Yeah. & E two equals get to over. I'm sorry. This is multiplying. Okay. So and that is you go to the bar to musical to Cuban. Uh Our 245. Mhm. Okay. Oh all right. Yeah. So that is all for this question and thank you for watching.


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