Euclidean 4dimensional electromagnetism

Whit Time (zeropoint) energy

Euclidean 4dimensionalelectromagnetismaretogetherwhitelectrogravitationandhyperspacetheoryaunifiedfieldtheorythathopefullycandescribemostthings. Itisthistheorythatyouusewhenyou areconstructing time (zeropoint) energyconverters (antilenz-generators).

According toeuclideanrelativityeverything is moving atlightspeedin the 4spaceaccording to theequationvx2+vy2+vz2+vt2=c2wherevx=dx/dTisthex-component of the velocity ,vy=dy/dTis the y-component of the velocity ,vz=dz/dTis the z-component of the velocityandvt=cdt/dT=√(c2-v2)is the time velocity ,cis thelightspeed ,tiscoordinatetimeand T own time. Chargeandcurrentdensityequationsbecomesjx2+jy2+jz2+(ρ0vt)2=(ρ0c)2wherejx=(d2I)/(dydz)isthex-component of the currentdensity ,jy=(d2I)/(dxdz)isthey-component of the currentdensity , jz=(d2I)/(dydx)isthez-component of the currentdensityandρ0=(d3Q)/(dxdydz)is thecharge densitywhereQ is thechargeandI=dQ/dTis thecurrent Qv=Ilwherelis thelength of the conductor

Jx=ρ0vx Jy=ρ0vy Jz=ρ0vz

Themagneticalfieldsandtheelectrostaticalfield/cbecomesfollowing

Bxy=μ0∫jxdy Bxz=μ0∫jxdz Bxct=μ0∫jxcdt

Byx=μ0∫jydx Byz=μ0∫jydz Byct=μ0∫jycdt

Bzx=μ0∫jzdx Bzy=μ0∫jzdy Bzct=μ0∫jzcdt

Esx/c=μ0∫(ρ0vt)dx Esy/c=μ0∫(ρ0vt)dy Esz/c=μ0∫(ρ0vt)dz

WhereBxyisthemagneticfield fromcurrentsflowing inx-directionin they-direction ,Bxzisthemagneticfield fromcurrentsflowing inx-direction in thez-direction ,Byxisthemagneticfield fromcurrentsflowinginy-direction in thex-direction , Byzisthemagneticfield fromcurrentsflowing iny-direction in thez-direction , Bzxisthemagneticfield fromcurrentsflowing inz-direction in thex-direction , Bzyisthemagneticfield fromcurrentsflowing inz-direction in they-direction.

PleaseobservethatI amusingstraightfieldlines from theconductorsinstead ofusingconcentretic rings,ifyou want touseconcentretic ringsyouhave tothinkthattheyareperpendicularagainstboth thecurrentand mystraightfieldlines.

Bxctisthemagneticfield fromcurrentsflowing inx-directionin the time dimension ,Byctisthemagneticfield fromcurrentsflowing iny-direction in the time dimension , Bzctisthemagneticfield fromcurrentsflowing inz-direktion in the timedimension , Esx/cistheelectrostaticfield/c in thex-direction , Esy/cistheelectrostaticfield/c in they-direction , Esz/cistheelectrostaticfield/c in thez-direction

Φxy=∬Bxydxdy Φxz=∬Bxydxdz

Φyx=∬Bxydydx Φyz=∬Bxydydz

Φzx=∬Bxydzdx Φzy=∬Bxydzdy

WhereΦxyisthemagnetic flux fromcurrentsflowing inx-direction in thexy-plane ,Φxzisthemagnetic flux fromcurrentsflowing in x-direction in thexz-plane , Φyxisthemagnetic flux fromcurrentsflowing iny-direction in thexy-plane , Φyzisthemagnetic flux fromcurrentsflowing iny-direction in thezy-plane , Φzxisthemagnetic flux fromcurrentsflowing inz-direction in the xz-plane , Φzyisthemagnetic flux fromcurrentsflowing inz-direction in thezy-plane

E2=Ex2+Ey2+Ez2+Ect2

Ex=∫(d(Esxcdt)/cdT)-∫(d(Byxdy)/dT)-∫(d(Bzxdz)/dT)=vt2Esx/c+∫(dEsx/(cdT))cdt-(vyByx+∫(dByx/dT)dy)-(vzBzx+∫(dBzx/dT)dz)=vt2μ0∫(ρ0vt)dx+μ0∬(d(ρ0vtdx)/dT)cdt-(vyμ0∫jydx+μ0∬(d(jydx)/dT)dy)-(vzμ0∫jzdx+μ0∬(d(jzdx)/dT)dz)

Ey=∫(d(Esycdt)/cdT)-∫(d(Bxydx)/dT)-∫(d(Bzydz)/dT)=vt2Esy/c+∫(dEsy/(cdT))cdt-(vxBxy+∫(dBxy/dT)dx)-(vzBzy+∫(dBzy/dT)dz)=vt2μ0∫(ρ0vt)dy+μ0∬(d(ρ0vtdy)/dT)cdt-(vxμ0∫jxdy+μ0∬(d(jxdy)/dT)dx)-(vzμ0∫jzdy+μ0∬(d(jzdy)/dT)dz)

Ez=∫(d(Eszcdt)/cdT)-∫(d(Bxzdx)/dT)-∫(d(Byzdy)/dT)=vt2Esz/c+∫(dEsz/(cdT))cdt-(vxBxz+∫(dBxz/dT)dx)-(vyByz+∫(dByz/dT)dy)=vt2μ0∫(ρ0vt)dz+μ0∬(d(ρ0vtdz)/dT)cdt-(vxμ0∫jxdz+μ0∬(d(jxdz)/dT)dx)-(vyμ0∫jydz+μ0∬(d(jydz)/dT)dy)

Ect=∫(d(Bxctdx)/dT)+∫(d(Byctdy/dT)+∫(d(Bzctdz/dT)=vxBxct+∫(dBxct/dT)dx+vyByct+∫(dByct/dT)dy+vzBzct+∫(dBzct/dT)dz=vxμ0∫jxcdt+μ0∬(d(jxcdt)/dT)dx+ vyμ0∫jycdt+μ0∬(d(jycdt)/dT)dy+vzμ0∫jzcdt+μ0∬(d(jzcdt)/dT)dz

WhereEistheelectricfieldExis thex-component of the electricfield ,Eyis they-component of the electricfield , Ezisthez-component of the electricfieldandEctis the time component of the electricfield. The force on a charge isF=QE

μ0isthemagneticconstant

U=∫Exdx+∫Eydy+∫Ezdz+∫Ectcdt=μ0∬(ρ0vtcdt/dT)(dx2+dy2+dz2)-μ0∬( jxdx/dT)(dy2+dz2-(cdt)2)- μ0∬( jydy/dT)(dx2+dz2-(cdt)2)- μ0∬( jzdz/dT)(dy2+dx2-(cdt)2)whereUistheelectric potential W=QU is thespacetimeenergy forthe chargeQ

Uct=∫Ectcdt=∫(∫(d(Bxctdx)/dT) +∫(d(Byctdy/dT) +∫(d(Bzctdz/dT))cdt=∫(vxBxct+∫(dBxct/dT)dx+vyByct+∫(dByct/dT)dy+vzBzct+∫(dBzct/dT)dz)cdt=∫(vxμ0∫jxcdt+μ0∬(d(jxcdt)/dT)dx+ vyμ0∫jycdt+μ0∬(d(jycdt)/dT)dy+vzμ0∫jzcdt+μ0∬(d(jzcdt)/dT)dz)cdt

WhereUctis the potential in the time dimension andWct=QUctisthe potential time energy forthe chargeQ

Ux=∫Exdx=∬(d(Esxcdt)/cdT)dx-∬(d(Byxdy)/dT)dx-∬(d(Bzxdz)/dT)dx=∫(vt2Esx/c)dx+∬(dEsx/(cdT))cdtdx-∫(vyByx+∫(dByx/dT)dy)dx-∫(vzBzx+∫(dBzx/dT)dz)dx=vt2μ0∬(ρ0vt)(dx)2+μ0∭(d(ρ0vtdx)/dT)cdtdx-∫(vyμ0∫jydx+μ0∬(d(jydx)/dT)dy)dx-∫(vzμ0∫jzdx+μ0∬(d(jzdx)/dT)dz)dx=∬d(Esxcdt)/cdT)dx-dϕyx/dT- dϕzx/dT

Uy=∫Eydy=∬(d(Esycdt)/cdT)dy-∬(d(Bxydx)/dT)dy-∬(d(Bzydz)/dT)dy=∫(vt2Esy/c)dy+∬(dEsy/(cdT))cdtdy-∫(vxBxy+∫(dBxy/dT)dx)dy-∫(vzBzy+∫(dBzy/dT)dz)dy=vt2μ0∬(ρ0vt)(dy)2+μ0∭(d(ρ0vtdy)/dT)cdtdy-∫(vxμ0∫jxdy+μ0∬(d(jxdy)/dT)dx)dy-∫(vzμ0∫jzdy+μ0∬(d(jzdy)/dT)dz)dy=∬d(Esycdt)/cdT)dy-dϕxy/dT- dϕzy/dT

Uz=∫Ezdz=∬(d(Eszcdt)/cdT)dz-∬(d(Bxzdx)/dT)dz-∬(d(Byzdy)/dT)dz=∫(vt2Esz/c)dz+∬(dEsz/(cdT))cdtdz-∫(vxBxz+∫(dBxz/dT)dx)dz-∫(vyByz+∫(dByz/dT)dy)dz=vt2μ0∬(ρ0vt)(dz)2+μ0∭(d(ρ0vtdz)/dT)cdtdz-∫(vxμ0∫jxdz+μ0∬(d(jxdz)/dT)dx)dz-∫(vyμ0∫jydz+μ0∬(d(jydz)/dT)dy)dz=∬d(Eszcdt)/cdT)dz-dϕxz/dT- dϕyz/dT

U=Ux+Uy+Uz+Uct

Uxistheelectric potential inx-direction

Uyistheelectric potential iny-direction

Uzistheelectric potential inz-direction

Whitthistheoryyou caneasylisee that theinductionand thelenzlawis coming fromtwofullyseparatedmagneticfieldsandthat isthereforebyreversingthemagneticfieldthatgives thelenzlawispossible tobuildselfpowering generatorsthatispowered by the time dimension.The equationsalsoenablesFTL communicationwhitrotatingtransmittor fields (more ofthat in anotherarticlewhereiderivesthe lightspeed from theseequations).Ithinkthat theseequationsbetterdescribeselectromagnetismthanmaxvellheavysideequations.

c2=1/(ϵ0μ0)whereϵ0istheelectricconstant