1

00:00:00,120 --> 00:00:06,650

All right, so let us continue by calculating the force and to talk acting on a magnetic dipole.



2

00:00:08,190 --> 00:00:14,370

So please remember what happened for the electric dipole moment when we applied a constant electric



3

00:00:14,370 --> 00:00:14,760

field.



4

00:00:15,480 --> 00:00:22,050

So if this electric dipole was misaligned, we got two individual forces that compensated on average,



5

00:00:22,200 --> 00:00:29,910

but they allowed to reorient the electric dipole so that this dipole aligns with the constant electric



6

00:00:29,910 --> 00:00:30,300

field.



7

00:00:31,080 --> 00:00:35,490

And we had also derive the equations for this torque and for this force.



8

00:00:35,970 --> 00:00:40,830

And you could see when we have a constant electric field, then this gradient is zero, which is why



9

00:00:40,830 --> 00:00:42,080

the force is absent.



10

00:00:43,590 --> 00:00:47,600

Now, something very similar happens for the magnetic dipole moment.



11

00:00:47,970 --> 00:00:55,350

But first of all, we have to understand, we have to remind ourselves how the magnetic dipole moment



12

00:00:55,500 --> 00:00:56,490

is generated.



13

00:00:57,210 --> 00:01:03,780

And in the previous section, we have derived this magnetic dipole moment where we have considered a



14

00:01:03,780 --> 00:01:04,610

current loop.



15

00:01:04,830 --> 00:01:07,230

So we have circulating electrons.



16

00:01:07,260 --> 00:01:10,320

You see here in this plane, these electrons circulate.



17

00:01:10,330 --> 00:01:12,270

So there's a current circular current.



18

00:01:12,690 --> 00:01:20,070

And this magnetic dipole moment is given by the perpendicular vector that stands on this plane here.



19

00:01:20,280 --> 00:01:21,390

So by this vector and.



20

00:01:23,420 --> 00:01:30,620

So when we have these circulating electrons, you can see that, yeah, the electron itself is moving



21

00:01:30,620 --> 00:01:37,370

here along these directions and also T is always tangential to this to this circle here and here.



22

00:01:37,370 --> 00:01:39,270

It's pointing along the opposite direction.



23

00:01:39,650 --> 00:01:44,740

In fact, it's different for every every possible position on the edge of this disk here.



24

00:01:45,050 --> 00:01:51,320

But for simplicity, I will just discuss these two cases here and now since we have a moving charge.



25

00:01:51,710 --> 00:01:56,120

There is, of course, the Lawrence force because we also have this magnetic field everywhere.



26

00:01:57,350 --> 00:02:02,630

And if you think about it, the forces that will act on these electrons look like this.



27

00:02:03,350 --> 00:02:06,760

So this means they rotate this whole disc.



28

00:02:06,770 --> 00:02:11,870

So the trajectory of the electron or the current trajectory will be rotated.



29

00:02:12,470 --> 00:02:19,250

And therefore also this normal vector here will be rotated so that it aligns with the magnetic field.



30

00:02:19,760 --> 00:02:26,810

So this means like in the electric case, also here, the magnetic dipole moment aligns with this static,



31

00:02:26,990 --> 00:02:28,730

homogeneous magnetic field.



32

00:02:29,870 --> 00:02:35,900

And the equations that allow to describe this are also very similar compared to electrostatic.



33

00:02:36,560 --> 00:02:41,840

So it's just that we have to replace the electric dipole moment with the magnetic dipole moment.



34

00:02:42,770 --> 00:02:48,710

However, the derivation of these equations is a bit difficult, but also I think it's a bit of a bit



35

00:02:48,710 --> 00:02:52,850

boring because we know already that the same thing will happen as for electrostatic.



36

00:02:53,240 --> 00:02:55,100

So I will not go through this here.



37

00:02:55,610 --> 00:02:59,870

But as a hint, if you want to do it yourself, you have to consider the Lorentz force.