Most variables have units which are obvious, but E (electric field) and B (magnetic field) should be stated in terms of the Gaussian units used for derivations.
+--+
Limit CHECKS
Dimensional consistency :
From file "Howell - Variables, notations, styles for Bill Lucas, Universal Force.odt"
sub-sub-section "Dimensional analysis (Gaussian units)" :
As a convention here take [unit vectors, c] as dimensionless .
OK, as all terms reduce to the same unit dimensions.
All derivations below ignore permittivity & permeability for Gaussian coordinates, except that of F, which requires these factors to balance units?
Example : From "Howell - Key math info & derivations for Lucas Universal Force.odt"
sub-sub-section "E0pdv(POIo,t) = E0odv(POIo,t)"
Units of measure
Gauss's Law for a single point charge, in the particle reference frame (FRp) :
1) E0pdv(POIo,t) = E0odv(POIo,t)
= Q(particle)/Rpcs(POIo,t)^2*Rpch(POIo,t)
E units = (charge/length^2)
(ignoring permittivity & permeability for Gaussian coordinates)
dp[dt : E] units = (charge/length^2/time)
B units Example : From "Howell - Key math info & derivations for Lucas Universal Force.odt"
(ignoring permittivity & permeability for Gaussian units)
sub-sub-section "BTodv(POIp,t) = BTpdv(POIp,t) "
Generalized Ampere's Law :
BIpdv(POIp,t) = Vpnv(POIp)/c X E0pdv(Rpcv(POIp))
units = (length/time)*(charge/length^2)
= (charge/length/time)
dp[dt : B] units = charge/length/time^2
F (force) ignoring permittivity & permeability for Gaussian coordinates
from my correction to (4-06) and taking "c" as dimensionless
F(r,v,t) = F(r,v,t) = q*[ E(r,v,t) + v/cB(r,v,t) ]
units = charge*[ (charge/length^2) + (length/time)*(charge/length/time) ]
= charge^2/length^2 + charge^2/time^2
OOPS!! This doesn't work at all!!!
If I insert permittivity (ε) and permeability (μ) :
from : https://simple.wikipedia.org/wiki/Maxwell's_equations#The_structure_of_the_magnetic_field
ε = permittivity = F/m (F = Farads)
μ = permeability = W/(A*m) = Power /charge/length
= mass*length/time^3/ charge/length
E -= electric field = V/m
B = magnetic field = H (H = Henrys)