Here I will use Howells form of (4-8) :
25Aug2015 re-start equation entry at Lucas04_13
/$ 04_08 Bi(r,v,t) = (v/c)E0(r,t) ;
Check 04_08 Bi(r,v,t) = (v/c)Ei(r,t) ;
/%^% BIodv(POIo,t) = (Vonv(PART)/c)E0odv(POIo,t) ;
BIodv(POIo,t) = (Vonv(PART)/c)EIodv(Rocv(POIo),t) ;
/* This still leaves the static component of B as per (4-11)
/$ B(r,v,t) = B0(r,t) + Bi(r,v,t)
/%^% BTodv(POIo,t) = B0odv(POIo,t) + BIodv(POIo,t)
/****where B0 is dropped as it "... is not electrostatic in nature ..." (p67h0.4)
02Jan2016 Note : There is no magnetic particle in the system, so B0 = 0
Actually Im confused p67h0.3
PROBLEM - When is an induce field "real"? see the 6 equations in Lucas p64
Generalized Amperes Law -> "v" will be very different for different
reference frames.
- If I assume that the Bi field is the same in all reference frames, then
v is a velocity relative to WHAT?
- Presumably it must be relative to the E0 field?
From this, I conclude that Equation 1 - implies that
the B field DOES depend on the observer frame! So if :
- you moved with a point charge, you would see NO B induced field?
- a very high-speed passing observer would see arbitrarily large B fields?
- many observers moving past the point at different relative velocities
will see different B fields
Weird, I didnt think of these things. Reminds me that a constant current
in a wire has a B field, but no E field (which I hadnt thought of)!
Use same functional form for B0 & Bi? This has to be verified and justified!
given the induced versus static B fields.
/$ B(r´,t´)
= (v/c)E0(r´,t´) + (v/c)Ei(r´,t´)
= (v/c)[ E0(r´,t´) + Ei(r´,t´) ]
/%^% BTodv(POIp(t),t)
= (Vonv(PART)/c)E0odv(Rpcv(POIp),t´) + (Vonv(PART)/c)EIodv(Rpcv(POIp(t),t)
= (Vonv(PART)/c)[ E0odv(Rpcv(POIp),t´) + EIodv(Rpcv(POIp(t),t) ]
/*++++++++++++++++++++++++++++++++++++++
/*add_eqn "Question
04_13rev1
Total B magnetic flux density as induced from E0 + Ei
/$ B(r´,t´) = Bi(r - v*t,t) = (v/c)[ E0(r´,t´) + Ei(r´,t´) ]
/%^% BTdv(POIp(t),t) = Vonv(PART)/c[ E0pdv(POIp) + (EIpdv(POIp)=0) ] ???
/* ( OK simple, but I have questions. 10Jan2016
I assume B0 doesn't appear as there is no "other background" B source -
eg permanent magnet of other [charges, currents]. Or is B0 from E0?
PROBLEM - When is an induce field "real"? - depends on relative velocities
so different observers at different relative velocities
see different B fields at the same Point of Interest (POI)!!??