Euclidean 4dimensional electromagnetism
20/05/2014 23:09
Euclidean 4dimensional electromagnetism
Whit Time (zero point) energy
Euclidean 4dimensional electromagnetism are together whit electrogravitation and hyperspace theory a unified field theory that hopefully can describe most things. It is this theory that you use when you are constructing time (zero point) energy converters (antilenz-generators).
According to euclidean relativity everything is moving at lightspeed in the 4space according to the equation vx2+vy2+vz2+vt2=c2 where vx=dx/dT is the x-component of the velocity , vy=dy/dT is the y-component of the velocity , vz=dz/dT is the z-component of the velocity and vt=cdt/dT=√(c2-v2) is the time velocity ,c is the lightspeed ,t is coordinate time and T own time. Charge and current density equations becomes jx2+jy2+jz2+(ρ0vt)2=(ρ0c)2 where jx=(d2I)/(dydz) is the x-component of the current density , jy=(d2I)/(dxdz) is the y-component of the current density , jz=(d2I)/(dydx) is the z-component of the current density and ρ0=(d3Q)/(dxdydz) is the charge density where Q is the charge and I=dQ/dT is the current Qv=Il where l is the length of the conductor
Jx=ρ0vx Jy=ρ0vy Jz=ρ0vz
The magnetical fields and the electrostatical field/c becomes following
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
Where Bxy is the magnetic field from currents flowing in x-direction in the y-direction , Bxz is the magnetic field from currents flowing in x-direction in the z-direction , Byx is the magnetic field from currents flowing in y-direction in the x-direction , Byz is the magnetic field from currents flowing in y-direction in the z-direction , Bzx is the magnetic field from currents flowing in z-direction in the x-direction , Bzy is the magnetic field from currents flowing in z-direction in the y-direction.
Please observe that I am using straight field lines from the conductors instead of using concentretic rings, if you want to use concentretic rings you have to think that they are perpendicular against both the current and my straight field lines.
Bxct is the magnetic field from currents flowing in x-direction in the time dimension , Byct is the magnetic field from currents flowing in y-direction in the time dimension , Bzct is the magnetic field from currents flowing in z-direktion in the time dimension , Esx/c is the electrostatic field/c in the x-direction , Esy/c is the electrostatic field/c in the y-direction , Esz/c is the electrostatic field/c in the z-direction
Φxy=∬ Bxydxdy Φxz=∬ Bxydxdz
Φyx=∬ Bxydydx Φyz=∬ Bxydydz
Φzx=∬ Bxydzdx Φzy=∬ Bxydzdy
Where Φxy is the magnetic flux from currents flowing in x-direction in the xy-plane , Φxz is the magnetic flux from currents flowing in x-direction in the xz-plane , Φyx is the magnetic flux from currents flowing in y-direction in the xy-plane , Φyz is the magnetic flux from currents flowing in y-direction in the zy-plane , Φzx is the magnetic flux from currents flowing in z-direction in the xz-plane , Φzy is the magnetic flux from currents flowing in z-direction in the zy-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
Where E is the electric field Ex is the x-component of the electric field , Ey is the y-component of the electric field , Ez is the z-component of the electric field and Ect is the time component of the electric field. The force on a charge is F=QE
μ0 is the magnetic constant
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) where U is the electric potential W=QU is the spacetime energy for the charge Q
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
Where Uct is the potential in the time dimension and Wct=QUct is the potential time energy for the charge Q
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
Ux is the electric potential in x-direction
Uy is the electric potential in y-direction
Uz is the electric potential in z-direction
Whit this theory you can easyli see that the induction and the lenz law is coming from two fully separated magnetic fields and that is therefore by reversing the magnetic field that gives the lenz law is possible to build self powering generators that is powered by the time dimension. The equations also enables FTL communication whit rotating transmittor fields (more of that in another article where i derives the lightspeed from these equations). I think that these equations better describes electromagnetism than maxvell heavyside equations.
c2=1/(ϵ0μ0) where ϵ0 is the electric constant
