All right, so let us continue by calculating the force and to talk acting on a magnetic dipole.
So please remember what happened for the electric dipole moment when we applied a constant electric
field.
So if this electric dipole was misaligned, we got two individual forces that compensated on average,
but they allowed to reorient the electric dipole so that this dipole aligns with the constant electric
field.
And we had also derive the equations for this torque and for this force.
And you could see when we have a constant electric field, then this gradient is zero, which is why
the force is absent.
Now, something very similar happens for the magnetic dipole moment.
But first of all, we have to understand, we have to remind ourselves how the magnetic dipole moment
is generated.
And in the previous section, we have derived this magnetic dipole moment where we have considered a
current loop.
So we have circulating electrons.
You see here in this plane, these electrons circulate.
So there's a current circular current.
And this magnetic dipole moment is given by the perpendicular vector that stands on this plane here.
So by this vector and.
So when we have these circulating electrons, you can see that, yeah, the electron itself is moving
here along these directions and also T is always tangential to this to this circle here and here.
It's pointing along the opposite direction.
In fact, it's different for every every possible position on the edge of this disk here.
But for simplicity, I will just discuss these two cases here and now since we have a moving charge.
There is, of course, the Lawrence force because we also have this magnetic field everywhere.
And if you think about it, the forces that will act on these electrons look like this.
So this means they rotate this whole disc.
So the trajectory of the electron or the current trajectory will be rotated.
And therefore also this normal vector here will be rotated so that it aligns with the magnetic field.
So this means like in the electric case, also here, the magnetic dipole moment aligns with this static,
homogeneous magnetic field.
And the equations that allow to describe this are also very similar compared to electrostatic.
So it's just that we have to replace the electric dipole moment with the magnetic dipole moment.
However, the derivation of these equations is a bit difficult, but also I think it's a bit of a bit
boring because we know already that the same thing will happen as for electrostatic.
So I will not go through this here.
But as a hint, if you want to do it yourself, you have to consider the Lorentz force.