Two point charges of equal magnitude Q are held a distance d apar...

Question

Two point charges of equal magnitude Q are held a distance d apart. Consider only points on the line passing through both charges. (a) If the two charges have the same sign, find the location of all points (if there are any) at which (i) the potential (relative to infinity) is zero (is the electric field zero at these points?), and (ii) the electric field is zero (is the potential zero at these points?).

Accepted Answer

everyone in this problem. We have two charged particles with separation X. They have the same kind of charge and equal magnitude. Okay. We're going to consider an axis joining the two particles and we are asked to determine all points on the axis where the electric field is zero. Okay. And then were asked whether the potential and the electric potential will be zero at those points. Okay. Alright. So let's think about this. And we're talking about electric field to begin with. Okay, where is the electric field? 0? And we know that we can write the electric field. E. Is equal to K. And we have two charges. So Q one que chu over R squared in this case are is going to be related to the distance X. Okay. And our hat which is that unit vector? Now we think about this. We can also write this in terms of forces if you want to think of it in terms of forces. So F. Divided by Q. Um And let me maybe not put that as an equal sign. Maybe as a bracket equal sign. Okay, because this is just for one church. Um but you can think of the electric field being influenced by the forces um of these charges. Okay, let's try a little picture. Think about this some more. So we have two charges here. Charge one in church too. Okay, now if we were to draw the electric field, these are these charges have the same. They're the same kind of charge. Okay, so they're both either positive or both negative and they have equal magnitude. Okay, so let's say these are both positive charges then the electric field is going to be going away from the charge. Okay. So if we're drawing on the axis between them, the electric field is going this way. Okay. And it's going to have some magnitude based on the magnitude of the charge. Okay, this is also a positive charge. The electric field will also be going away and because this has this this charge has the same magnitude. These two field blinds have the same magnitude as well. Okay. Alright. So you can imagine these field lines coming out and what you'll see is that when you get to the midpoint between the two, you have field line going this way and you have a field line going this way and they have the same magnitude but opposite directions. Okay. And so they're going to cancel each other out. So at the midpoint of the two charges, We're going to have the electric field zero. Okay. So e the electric field is going to equal zero at the midpoint. Okay. And you can do a similar drawing for the opposite case where the charges are negative. Okay. If the two charges are negative then you have the same thing that you have your field lines going into the charge. Okay? But you will get the same thing at the midpoint, you have equal magnitude of charge opposite direction and they cancel. Okay. So you get a net electric field there? That is zero. Alright, now let's think about the second part. What about the electric potential? Is it going to be zero at this point? Okay, well recall that we can write the electric potential. V Okay. As 1/4 pi epsilon? Not Okay. Times the sum of Q I over ri Okay. And in this case we have two charges. So we're just going to add the two of them. Okay, so we have the first charge. Q one divided by R one plus Q two divided by R two. Okay. Alright now our charges are the same. Q one Is equal to Q two. Okay, No Q one and Q two are equal. That means that this term can never be zero. Okay, well and we know that R one and R two are the same as well. Okay, Q one. R one is the same as Q two over R two. These two terms are the same. So this term is never going to be zero. We know that 1/4 pi epsilon not is not zero. Okay, so that means that the electric potential is not zero at this point. Okay, So if we look at our solutions, we found that the electric field is going to be zero at the midpoint of the two charges but V is not zero. Okay, so that is going to be answered. Thanks everyone for watching. I hope this video helped see you in the next one.

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