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The " figure below shows two small, charged beads separated by a distance of d = 2.50 cm: The charges are 9, 20.0 nC and 92 25.0 nC. Point B is at the midpoint...

Question

The " figure below shows two small, charged beads separated by a distance of d = 2.50 cm: The charges are 9, 20.0 nC and 92 25.0 nC. Point B is at the midpoint between the two charges, and point A is at the peak of an equilateral triangle; with each side f length d,as shown: (Assume the zero of electric potential is at infinity: )60.09What is the electric potential (in kV) at point A? kV(b) What is the electric potential (in kV) at point B?

The " figure below shows two small, charged beads separated by a distance of d = 2.50 cm: The charges are 9, 20.0 nC and 92 25.0 nC. Point B is at the midpoint between the two charges, and point A is at the peak of an equilateral triangle; with each side f length d,as shown: (Assume the zero of electric potential is at infinity: ) 60.09 What is the electric potential (in kV) at point A? kV (b) What is the electric potential (in kV) at point B?



Answers

The two charges in Figure P25.12 are separated by $d=$ 2.00 $\mathrm{cm} .$ Find the electric
potential at (a) point $A$ and (b) point $B$ , which is halfway between the charges.

And the question. There are three point charges placed at the corners of an equal at a little green lateral triangle having sides up 2.1 question. So let's throw the figure that the cool lateral fangled yes do on each side have planned 1.5 m. Sorry, one 515 later. Is there a 0.5 m? And in a three corner? The charges are three point churches, so that is Q one. That's cute, you know, and also ask you. So in goes, and I have to find out that what is a total electric force on the to a point five micro cola charge? I don't know whether the 2.50 microphone charges placed. There are no information about that in questions. So the question is, the question is irrelevant. So we go to go. Should be that What is the electric potential energy of the three charges? So all of the point charges of one Columbus on Columbus so you can find that system potential of the system, Which is it recalls to one pie for a pie of silent night. Yeah, chill squared, divided by 015 and 23 So this constant, the value is right. Develop kings. So this is the potential of the system. The energy is 1.88 to 10 or 11 this event.

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.

16.12. So we have this configuration of charges and along with this point of interest A Here they form an equilateral triangle whose sides have the length of two centimeters. And so we'd like to find the voltage at points A and B B is directly halfway between them. We're going to use, um so I mean, let's just go ahead and get started. We're going to use the usual convention with, um, wait with point charges for where zero voltages was set it so that it zero infinitely far away. So you know, it's our cake. You over our. So let's start with this one. Actually, Nelson factor out the distance because it's the same in both cases and so that it's this negative 15 nano cool homes plus 27 nano cool ums. And since so evaluating this, we get a positive 5.39 kilovolts and then we would do pretty much the same thing here. Except now the distance is D over too, and in this case, because we're closer toe both charges, but we're still sort of equal distant between them and this positive charges larger so the overall potential is going to be positive, and because it's closer now, it's also going to be greater. Indeed, this is 10.8 kilovolts, which makes sense. It's twice as big as our 5.39 because we're now half the distance away from.

Here, we're going to look at an example of electric potential and electric potential energy for point charges. So the potential is V. Equals K. Q. Over our. So notice that there's only one charge in that. Um Whereas the energy there are two charges. So, potential energy involves the interaction between two charges, potential is the field of a single charge. So as a demonstration of this, we are going to find the potential between two differently charged objects right in between them. And so uh even if there were just one charge there, we could have a potential but we want to add the separate potentials of both the positive and the negative charge and that will evolve. K. That electrical constant times the separation which for right smack dab in the middle. Um That's going to be are over two. Um Mhm. We should call it distance, so it doesn't get confusing in there. Um And then we have Q1 plus two because there are two of those. Yeah. And just a reminder that a nano is 10 to the -9 in S. I. Units, So we'll have to put the charges in with 10 to the -9. Yeah. Yeah. Okay, so both charges are involved and they are both in nano columns. So if we work that out, the potential In the middle turns out to be 102.9V, the next thing we'll do is find the potential energy of the arrangement of charges. And for that we will be using The two point charge Formula with the two charges because potential energy is an interaction and we will have to use the full separation between the two. That unit will come out to be in jewels. Let me see that's a much smaller number. And it is negative. And you might wonder again, what is the significance of a negative potential energy? Um So a reminder that if this were an electrical, I'm sorry. If this were a gravitational potential energy, that negative would signify a bound system such as the moon in orbit around the Earth or the Earth and orbit around the Sun for that matter. So we are going to see the same interpretation is true in electricity, that the negative energy means that the two particles are bound to each other. So there is some sort of bond keeping them um together. Um Or we could just say that they are attracted to each other. Um But you can have two charges attracted. But if their potential energy in the system of their total energy is positive, they will not be bound. Yeah.


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