domingo, 26 de enero de 2020

potencial para-eléctric y para-gravitatori


potencial eléctric:
E_{e}(x,y,z) = kq·< x^{n}/(ct)^{n} , y^{n}/(ct)^{n} , z^{n}/(ct)^{n} >
V_{e}(x,y,z) = ( 1/(n+1) )·kq·(ct)·Q[n+1](x,y,z)
E_{e}(x,y,z) = grad[ V_{e}(x,y,z) ]


flux[ ∫ [ grad[ V_{e}(x,y,z) ] ]·< d[x],d[y],d[z]> ] = ( 1/(n+1) )·kq·Q[n](x,y,z)·xyz
div[ ∫ [ E_{e}(x,y,z) ]·< d[x],d[y],d[z]> ] = kq·Q[n](x,y,z)


potencial gravitatori:
E_{g}(x,y,z) = (-1)·kq·< x^{n}/(ct)^{n} , y^{n}/(ct)^{n} , z^{n}/(ct)^{n} >
V_{g}(x,y,z) = (-1)·( 1/(n+1) )·kq·(ct)·Q[n+1](x,y,z)
E_{g}(x,y,z) = grad[ V_{e}(x,y,z) ]


flux[ ∫ [ grad[ V_{g}(x,y,z) ] ]·< d[x],d[y],d[z]> ] = (-1)·( 1/(n+1) )·kq·Q[n](x,y,z)·xyz
div[ ∫ [ E_{g}(x,y,z) ]·< d[x],d[y],d[z]> ] = (-1)·kq·Q[n](x,y,z)


ecuacions de camp:
flux[ ∫ [ grad[ V_{e}(x,y,z) ] ]·< d[x],d[y],d[z]> ] = ∭ [ div[ ∫ [ E_{e}(x,y,z) ]·< d[x],d[y],d[z]> ] ] d[x]d[y]d[z]
flux[ ∫ [ grad[ V_{g}(x,y,z) ] ]·< d[x],d[y],d[z]> ] = ∭ [ div[ ∫ [ E_{g}(x,y,z) ]·< d[x],d[y],d[z]> ] ] d[x]d[y]d[z]

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