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So in the previous lectures, you have already seen that magnitude Static's is quite related to electrostatic,



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and the same is also true for the energy and magnetic aesthetics.



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So I want to keep this lecture quite short and just show you the yeah.



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The energy expressions and will not really drive them because this is easily done by analogy with the



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electrostatic equations.



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So we start again from the continuity equation for the energy density that we have derived and one of



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the first lectures of this course.



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So we have higher energy density that enters this continuity equation.



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So when we recap the electrostatic that we had here, consider only the electric field contribution.



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So now we only consider here the magnetic field contribution and the total energy is now just the integral



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over this density, which is basically this expression.



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And this is a fine result if we already know our magnetic field, for example, for the magnetic dipole



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and the previous lecture, we could just go ahead and calculate this.



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But sometimes you do not even have to calculate the magnetic field.



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You just have your.



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Yeah, your your current profile.



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And so what you can do then is use introduced as this vector potential AI and use one of these Maxwell's



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equations.



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So this is very similar to what we have done in Electrostatic, where we have ended up with this energy



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here that included just the charge profile and the electrostatic potential.



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And so obviously we get here very similar results.



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We get here the same integral, but the integral is now the current distribution, which is this one



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instead of that one here and we have here and the DOT product with the vector potential instead of the



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scale of potential.



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So this is how you calculate the energy in Varnado Static's.