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So in the last lecture, I have discussed that we have now a differential equation for our Victa potential



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that looks just like the song equation and that we can carry over all of the results to easily determine



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the vector potential A and A magnetic field B and the equation we will get is called the bias of our



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law.



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So we have here our differential equation that looks just like the song equation and the solution from



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Electrostatic who looked like this.



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So if you remember, we did it in the following way.



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We considered a point charge or charged sphere, a single one, and then we calculated the electrostatic



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potential fine and the electric field e and then we generalize this result by considering many charged



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spheres, which gave us some of these individual potentials here.



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And if we made our spheres smaller and smaller so that we ended up with a charged density instead of



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individual charges, we transform the sum to the integral.



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And this was the result.



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The corresponding electric field looked like this because it is just.



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Yeah, the little gradient of this file.



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Now we take these results and carry it over for the differential equation of a and then we can also



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determine, B, why this relation here?



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So you can see the solution for the vector potentially looks very similar to the solution for the electrostatic



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potential fire.



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The difference is that instead of this constant one over Epsilon zero, we have now here Ammu zero,



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which of course comes from this factor and this factor here instead of the scalar charge danceteria,



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we have now the vector, which is the current density Jaafar, which is here now, the magnetic field



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B is just the rotation of A instead of the minus gradient here.



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So the solution is here that the magnetic field is Muzio over for PI and then we have the integral of



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the current density time and then the crust product of this vector here and divide it by the distance



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in the position vectors to the power of three.



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And we integrate over the whole space in all cases.



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And so this law is called the Bill Savala.



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And it's really helpful because if we have some current some current loop, for example, we can easily



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calculate the magnetic field by calculating this integral here.