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Energy & Torque of Dipole Moments

Patrick Ford
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All right, everyone, welcome back. So in the last video, we saw that an electric dipole has something called a dipole moment in between the two charges. Well, now we're going to see what happens if you put it in electric field. Specifically, what happens to the energy? Let's check it out. So we put in electric dipole inside of under Uniform Electric field. It picks up a potential energy, and it's because basically the charges wants to start moving around. And this potential energy right here is given is this fancy little equation, which is like a dot product between two vectors. But the more common expression that you'll see and the one that will be working with is this p e co sign of data. So the way I like to remember this is think back to when we're working in physics, one with a work where you have, like, a force off of in this direction. And if we had a distance in this direction, de then if we could figure out the angle between them theta, then the work was just equal to F D co sign of data. It's kind of similar to that. We just need the components of the dipole moment that is in the same direction as the electric field. So we're gonna use the cosign of data. And for this torque, the reason that picks up a torque A di poll experiences a torque and electric field. Because if you think about the uniformed electric field, let's say I had uniform electric field pointing upwards like my fingers right here, and you had an electric dipole that was made up of a positive and a negative charge. And we knew that the dipole moment between them was P. Well, if you have P, which is the dipole moment and you have the electric field and what happens is we know positive charges, want to move upwards, and electric fields and negative charges want to move downwards. So what happens if you have this electric field right here? And this pen represents this die poll? The left charge wants to move up, and the right charge wants to move down, and we'll start to spin this whole entire thing. So that's called a torque. It's creates like a rotational motion, And this is why Di polls experience torque insides of fields and So just like we worked with torques back in physics one, we just used the Costa or sorry, the instead of the coastline, we used the sign of theta to describe the magnitude of that torque. And that's basically the two equations that you need to know. So again, let's go ahead and work out a very quick example. So we have a die poll that's depicted in this figure below were told that there is a uniformed electric field of 200 Newtons per cool, um, and we're told to find what the potential energy is of the type hole. So in part A, we're gonna be figure out what the potential energy is. So we have two choices we could use p dot e or we could use negative p e CO sign of data. So we're gonna use negative p e o co sign of data because we have this angle right here that we're working with. So we know what the electric field is, and we just have to figure out what the angle between the dipole moment is and the electric field. So we actually very careful about this. Remember that the electric typo points from the distance vector. Uh, it points from the positive charge all the way to the negative charge. In other words, this vector right here is actually our dipole moment. So we need to figure out what the what the co sign or with the angle is between the electric field and the dipole moment. Now, thankfully, in this figure, this actually is this 30 degrees. So we actually do know what the cosine of this angle is. So I just want to warn you, because if this was the opposite, if this was actually like this, if this was actually backwards and the dipole moment was like this, the angle would not be 30 degrees. It would actually be negative 30 degrees. Okay, so don't get that confused. So it's like this. So you just have to be careful, and then we just have to figure out what the actual dipole moment is, right? So we gotta have to go figure out what that is. So the dipole moment is just going to be the magnitude is just gonna be Q times D. Well, that dipole moment is just the charges involved, which is the one Cool, um, times the distance. But remember, everything has to be in the right units. We have to have meters. Things like that, this is given is one centimeter as the distance vector between these two things. So that means that we're just gonna use 0.1 in terms of meters. Okay, so we're just gonna get 0.1 And now we can go ahead and stick it inside of the potential energy. So that means that our potential energy is just equal to negative. We got 0.1 We've got the electric field, which is 200 then we've got the co sign of feta. So the coastline of three data is the co sign of 30. And if you work this all out, you should get a potential energy of negative 1. jewels. OK, so now let's look at part B. Part B is asking this to figure out what the torque is, and we're just gonna use the p e sign of data, and that's it. That's all we're gonna dio. So we know that the torque and we're by the way, were asked for the magnitude of the torque so with this, torque is usually given as a vector. But we can just figure out the magnitude by using this equation right here. We don't really have to worry about the direction. So the magnitude is just gonna bpe cosign data or sorry, sign data and we already have it. All those numbers are so let's go and plug them in. So the torque is just equal to 0.1 For the dipole moments, electric field is 200 now the sign of 30 is gonna give us our answer. So it means that the Tao the torque is just gonna be one, and that's gonna be Newton meter. And that's basically our answers. So we got one Newton meter for the torque, and then we've got the potential energy of negative 1.73 jewels. Don't worry about the fact that the potential energy is negative, because that just means that we're really only interested in the change in potential energy and versus kinetic energy. Alright, So don't don't get too preoccupied about the negative sign there. Alright, guys, let me know if you have any questions