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Two point charges Q1 +4.10 nC and Q2 -2.40 nC are separated by 45.0 cm What is the electric potential at a point midway between the charges?(b) What _is the potenti...

Question

Two point charges Q1 +4.10 nC and Q2 -2.40 nC are separated by 45.0 cm What is the electric potential at a point midway between the charges?(b) What _is the potential energy of the pair of charges?What is the significance of the algebraic sign of your answer? Positive work must be done to separate the charges Negative work must be done to separate the charges_

Two point charges Q1 +4.10 nC and Q2 -2.40 nC are separated by 45.0 cm What is the electric potential at a point midway between the charges? (b) What _is the potential energy of the pair of charges? What is the significance of the algebraic sign of your answer? Positive work must be done to separate the charges Negative work must be done to separate the charges_



Answers

Two point charges $Q_{1}=+5.00 \mathrm{nC}$ and $Q_{2}=$ $-3.00 \mathrm{nC}$ are separated by 35.0 $\mathrm{cm} .$ (a) What is the electric potential at a point midway between the charges? (b) What is the potential energy of the pair of charges? What is the significance of the algebraic sign of your answer?

For this problem on the topic of electric potential, we have two point charges Q one and Q two with magnitudes five nano columns and minus three nano column respectively, which are separated by 35 centimeters. We want to firstly find the potential energy for the pair and then find the electric potential at him at the midway point between the charges. So firstly the potential energy you is equal to the product of charges which is Q one times Q two over four pi. Absolutely not James R, which is equal to the product of charges five times 10 to the minus nine columns, times minus three times 10 to the minus nine columns, times 1/4 pi epsilon, not which is 8.99 times 10 to the nine newton meters squared, McCullum squared, all divided by the separation between the charges zero 0.35 meters, which gives us electric potential energy of minus of minus three 0.86 times 10 to the minus seven jules. Now the minus sign here means that it takes 3.86 times 10 to the minus seven jewels to pull the two charges apart from 35 centimeters to a much larger separation. Next for part B. We want to find the potential at the midpoint between the two charges. The potential is equal to the potential due to charge one, which is Q one over four Pi absolute not are one that's the potential due to charge to which is cute too. Over four pi absolute not R two. And so this is in charge of five times 10 to the minus nine column will suppress the units here, times 8.99 times 10 to the nine divided by the distance of the midpoint is 0.175 meters. Last the same for charge too, which is minus three times 10 to the minus nine columns, tens, electric constant, 8.99 times 10 to the power nine Inessa units. And again the distance of the midpoint is 0.175 m, so we get the potential electric potential at the midpoint to be 103 vaults.

It's custom we have this configuration as Joan is a plot. We have a positive church off 2.4 dental. Ah, Nana Colon. And we have a negative charge that is elective 6.5 minute Colin. And we have point A and point B is can be seen from Graff. So we want, you know, support the potential between a and put a interpretation, put B and the potential difference between sometimes and from Zep retention difference. What we can find is the work done on a church where it moves frumpy trait. So in section three, Section three of of Chapter 18 what we learned inside so potential of different of At a certain point, there's a superposition of the potential cost by or different sources. So say the protection and a It will be a some off the potential cost Buy balsa points to a church in collective charge. So I have the equals K Q one over r, um, are a cost. I won because this's just for Miller for as a protection to tricycle charge just take you to over our a caused by too. Okay, so K is Larry Times Tent is nice Mitre Square, Coolum Square are s a R v i R E mine. Alright, you are actually the same. It's the same distance is always a point of 05 meter. So I will combine these two numbers and finally que um, ask you to is 2.4 times 10 to the negative sign of cool. Um minus 6.5 can times 10 to the next nine and 1/4 just gives me a value of negative seven, hundreds of 30 still votes. So it's very natural. Concert is to be expected because both charges are the same distance away from eight but selective charges much more negative than positive church. So the total potential will be inactive. And this look att p b we have it's the same scene and we also have kinky one over are a one plus cakey R B one. Ask a cue to over our Peter nausea off different distances. So now I can't just simply put the same denominator. I have to use different denominators. I still have nine times 10 to the Knights and cue one over R B one is 2.5 times 10 to the and to flank them. Two by two by 0.8 Bender minus 6.50 times. Tent is nice. Colin, over 7.60 meters. Says skips a selective 704 votes. Okay, um great. Now we look at Proceeded. Asks us what isthe Ah, work down. If we want to have a charge of 2.5 Coolum symbols from B to A. So the work is charged hunks of potential difference. And the charge is 2.50 times 10 to the negative light Colin. And so potential is there active Silvano Four votes minus Conectiv threesome. 73 seven votes. And this gives us 8.2 times. Tent is elective eight. Just so. That is the work done by the electric field as a charge where travels from point B to point a

So in this problem we have thes two point charges on we have thes two points that defined near the point churches and we have their distances from each other labeled as well. So what we want to do is the first part of this problem. You want to find the potential at point A and point B. So it's the first two things that we're gonna look at. So in order Thio to do this we need to use is the formula for potential due to a collection of point charges. What that formula looks like is Aziz follows. So we have potential equal to Colom's constant times. The sum a summation off the charge, divided by the distance from the point that we're looking for the potential. So using this formula, we're gonna apply it to our first two parts. So we want to find the potential at 20.8. So if we go ahead and write this out, we'll have our constant upfront and we have key one, which is equal to 2.4 nano columns, and I'm writing Nano columns here. But really, when we're doing the math, we want to use 2.4 times 10 to the negative Ninth. Since this constant right here has cool arms in the unit, we're going to divide that by the distance of from Q 12 point a on that's 0.5 m. And then we're gonna add negative 0.65 Nano McCullum's divided by 0.5 since it's the same distance from Point A, and the unit comments still applies here to 6.5 Nano columns as well on Let me just write down the constant for you columns. Constant that is going to be 8.99 times 10 to the ninth. Newton's tennis meters squared her Coolum squared. This is the value of our constant, and now we can plug in and solve. And when we do that, we'll get potential of negative 737 volts. So now for Part B, we're gonna do the same thing. We're just going to change. Basically, these these distances values for our since Q one and Q two are different separation away from point B. So it will have baby the potential appoint feed, writing at our constant on multiplying that by the some, which will be 2.4. You know columns divided by 0.8 That's the distance between Q one and be, and we'll have negative 6.5 Nano Colom's Divided by 0.6 and South a distance between Q two and B. And just remember to convert to Kellems for these two charges. And when you go ahead and calculate, we'll find that the voltage at point B is negative. 704 volts. So now that we found the potential at Point A and Point B on the third part of this problem were asked to find the work that is done from moving a charge from Point B to point A where this charge, um, has a value of at 2.5 net McCullum's and this is a positive charge. So in order to do this to find the work that's done to move this charge from Point B to point A, the formula that we're gonna use is the one that relates work to potential. So this formula looks like this will have the work done from moving the charge from point B to point A. It's gonna be equal to keep out the charge times the potential at point B minus thedc potential appointing. Because when we, uh, bring this over, expand this out. What we end up getting is the potential energy, which is equal to the work. That difference in potential energy will be equal to the work done. So now we can go ahead on bond plug in. We'll go ahead and write out 2.5 times 10. It's the negative ninth cool arms, the actual number that you're gonna plug into your calculator times minus 704 minus negative, 737 and should always be careful with checking the, uh, negative and positive values sign your values are. So once we do that, we find that the work needed to move that charge from point B to 0.0.8 is positive. 8.2 times 10 to the negative eighth jewels. So So that shows that a new electric force does positive work on a positive charge when moving from a higher to a lower potential

Hi in the given problem there are two charges bless human and minus you too. Which are having the values Cuban is less. 2.40. No, no problem. And you too is -6.50 nano Ghulam. The gap between them it's given as 0.100 m are is equal to. Then there is a .8 exactly in the middle of the charges. So these distances will be 0.05 m each and another point B. Whose distance from this Cuban is 0.080 m. And from you to this is little point 060 m. No. In the first part of the problem we have to find the potential at point A. And that will be because of the two charges. What will be given by K into Cuban Divided by this 10 0 x 0.0. Why meter plus key? You do If I can find The same distance 0105 m. Taking this. Yeah, whose value is nine into 10. They should part nine and taking it, woman living behind the value of Cuban, It is 2.40 Nano. and for Nano This is -910 for -9. Invited by uh 0.05. We have already seen 10 plus it will be -6.50. No no again so Again and it's part -9 Having the same dispense 0.5 0.05 m now taking this And it's par -9. Also as a foreman out And 2.40 divided by 0.05 will come out to be 30 -6.50 divided by 0.05. It will come out to be 100 and eat point three. Sorry you have then the wrong calculations here actually it will come out to me for the And here the second term will come out to be hunted and part and that will be involved Cancellelling this tentage purpose nine. The tented for -9. Finally we get the potential at point A. To be equal to -738. Or which is the answer for the first part of the problem. No The 2nd part of the problem we have to find now potential at the point B. And again that is because of the two charges one Cuban and another two. So that is he into cuba by the distance 0.08 m last year you do By 0.06 m. So taking this K. As a comin out Which is 19 to 10 days par -9. Last nine. And then putting the value of Cuban which is 2.40 Into 10 for -9 Divided by 0.08. Yes The value of Q two Which is -6.50 In to tenders for -9. Again Divided by the distance which is 0.0 six m taking this and mine And this 1 -9 also has a comin out. He kept 2.40 divided by 0.08 -6.50 Divided by 0.0 six. So it will be nine under bracket. This is party minus 108.3 war. Well finally is potential. We be I'm supposed to be -705 4 which is answered for the second part of the problem. No In the 3rd and the last part of the problem We are taking a third charge you three which is positive 0.50 nano column. As his potential will be Is more than -738 means is more than eight. So the electric field will do a positive work as a positive charge is being shifted from the two A. Is from high potential to low potential. So work done is equal to Q into potential difference, This is Q3, This is we be minus were. And finally this was done. 2.50 into 10 for -9. Or maybe this is -705- or via. This is -738. But this is 2.50 Into 10 for -9. Or finally adding all these things. The final answer is it will come out to be positive and this is 82.5 Into 10 days apart minus mind you'll or 8.25 and two And this one minus jewels. Which is the answer for the third. In the last part of this problem, thank you.


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