So in the previous lectures, you have already seen that magnitude Static's is quite related to electrostatic,
and the same is also true for the energy and magnetic aesthetics.
So I want to keep this lecture quite short and just show you the yeah.
The energy expressions and will not really drive them because this is easily done by analogy with the
electrostatic equations.
So we start again from the continuity equation for the energy density that we have derived and one of
the first lectures of this course.
So we have higher energy density that enters this continuity equation.
So when we recap the electrostatic that we had here, consider only the electric field contribution.
So now we only consider here the magnetic field contribution and the total energy is now just the integral
over this density, which is basically this expression.
And this is a fine result if we already know our magnetic field, for example, for the magnetic dipole
and the previous lecture, we could just go ahead and calculate this.
But sometimes you do not even have to calculate the magnetic field.
You just have your.
Yeah, your your current profile.
And so what you can do then is use introduced as this vector potential AI and use one of these Maxwell's
equations.
So this is very similar to what we have done in Electrostatic, where we have ended up with this energy
here that included just the charge profile and the electrostatic potential.
And so obviously we get here very similar results.
We get here the same integral, but the integral is now the current distribution, which is this one
instead of that one here and we have here and the DOT product with the vector potential instead of the
scale of potential.
So this is how you calculate the energy in Varnado Static's.