First term This expression seems to violate the statements in the previous paragraph!? "... linear superposition does not hold for the Bv generated fields ..." Magnetic field arising from single moving point charge : https://en.wikipedia.org/wiki/Biot%E2%80%93Savart_law from Maxwells equations : /$ ET = q/4/π/ε0*(1 - v^2/c^2)/(1 - v^2*sin(θ´)^2/c^2)^(3/2)*r´h/|r´|^2 B = 1/c^2*vET /%^% E = Q(particle)/4/π/ε0*(1 - Vonv(PART)^2/c^2)/(1 - Vonv(PART)^2*sin^2(Op)/c^2)^(3/2)*rhp/|rp|^2 B = 1/c^2*Vonv(PART)E /* where rhp is the unit vector pointing from the current (non-retarded) position of the particle to the point at which the field is being measured, and Op is the angle between v and rp. for v^2 << c^2 /$ ET = q/4/π/ε0*r´h/|r´|^2 B = μ0/4/π*q*vr´h/|r´|^2 /%^% E = Q(particle)/4/π/ε0*rhp/|rp|^2 B = μ0/4/π*Q(particle)*Vonv(PART)rhp/|rp|^2 /* Jackson 1999 p782h0.15 Table 3 provides conversions (here to Lucas's Gaussian units, except p180h0.45 under (A-11) he uses CGS units?)) /$ ET = 1/4/π/ε0*q *r´h/|r´|^2 * (4*π*/ε0)^(0.5) = (4*π*ε0)^-0.5*q *r´h/|r´|^2 ??? */??? B = μ0/4/π *q*vr´h/|r´|^2 / (4*π/μ0)^(0.5) = (μ0/4/π)^ 0.5*q*vr´h/|r´|^2 /%^% E = 1/4/π/ε0*Q(particle) *rhp/|rp|^2 * (4*π*/ε0)^(0.5) = (4*π*ε0)^-0.5*Q(particle) *rhp/|rp|^2 B = μ0/4/π *Q(particle)*Vonv(PART)rhp/|rp|^2 / (4*π/μ0)^(0.5) = (μ0/4/π)^ 0.5*Q(particle)*Vonv(PART)rhp/|rp|^2 /* NUTS - "units" dont work out (μ0,4,π,ε0) Here, B = B0(r´,v´,t´), and substituting c for (μ0/4/π)^0.5 as "patch" until I understand the conversions better /$ B0(r´,t´) = q/c*(vr´h)/|r´|^2 /%^% B0(Rpcv(POIp),t´) = Q(particle)/c*(Vonv(PART)rhp)/|rp|^2 /* Second term vovEi(r´,t´) immediately, the second term is wrong, as "/c" has been dropped, or (4-13) is wrong. Notice that this second term is a consequence of the [static, induced] split of [E,B], as per (4-11) which I still have to check. Use : /$ v/cEi(r´,t´) /%^% Vonv(PART)/cEIodv(Rpcv(POIp(t),t) /* Combined expression /$ B(r´,t´) = q/c*(vr´)/|r´´|^2 + v/cEi(r´,t´) /%^% BTodv(POIp(t),t) = Q(particle)/c*(Vonv(PART)Rpcv(POIp))/|r´´|^2 + Vonv(PART)/cEIodv(Rpcv(POIp(t),t) /*++++++++++++++++++++++++++++++++++++++ /*add_eqn "Lucas_typo_or_omission 04_14 B&E point charge - substituted Amperes law /$ B(r´,t) = q/c*(vr´h)/r´s^2 + v Ei(r´,t´) B(r´,t) = q/c*(vr´h)/r´s^2 + v/cEi(r,t) /%^% B(Rpcv(POIp),t) = Q(particle)/c*(Vonv(PART)rph)/rps^2 + Vonv(PART) EIodv(Rpcv(POIp(t),t) BTpdv(POIp,t) = Q(particle)/c*(Vonv(PART)Rpch(POIo(t),t))/Rpcs(POIo(t),t)^2 + Vonv(PART)/c(EIpdv(POIp)=0) /* OK - simple, but Lucas is missing c in 2nd term (check Jackson) 10Jan2016 Lucas's units don't balance! (uses Gaussian units...)