RECIPROCAL SYSTEM DATABASE Status Report: An Aperiodic Blog

January 20, 2012

Distinction Between Coulomb_q and Coulomb_Q

Filed under: Science — transpower @ 11:35 pm

In the very first publication on the Reciprocal System, The Structure of the Physical Universe (1959), Dewey B. Larson taught us to distinguish between electrical quantity, q, and electrical charge, Q.  In the Reciprocal System, an electron may have zero charge or unit charge; there are no other possibilities.

1 uncharged electron = 1.602062 x 10-19 coulombs_q, with dimension = s (electrical quantity)

1 charged electron       = 1.602062 x 10-19 coulombs_Q, with dimension = t/s (electrical charge)

This distinction is of utmost importance in working with capacitors.  Capacitors are known to be electrically neutral.  Conventional physics says that capacitors store charge, with an equal number of negative and positive charges, so that the net charge is zero.  The Reciprocal System says, no, capacitors store uncharged electrons.

The definition of capacitance in SI units is

1 farad = 1 coulomb_q / 1 volt

The coulomb here is the coulomb of quantity, coulomb_q, because a capacitor actually stores uncharged, massless electrons.  In terms of Reciprocal System space-time dimensions, the above definition translates to

s3 / t  = (s) / (t/s2)

So the cgs unit for capacitance, cm, cannot be correct.  Previous work on the Reciprocal System used the cm (s) as the unit of capacitance; this now seems to be wrong.  Also, using electrical charge, coulombs_Q, t/s, in the above equation instead of s on the right would give capacitance as s, which is now seen as incorrect.  This error can be traced by the definition of capacitance for a parallel plate capacitor as the dielectric constant (of the dielectric) times the area of one of the plates, divided by the distance between the plates.  In cgs, the dielectric constant is dimensionless, but it is not so in the Reciprocal System:  it must be included in the dimension of capacitance.

The SI definition of time constant for a DC RC circuit is

tau = R x C

In Reciprocal System space-time dimensions, this is

tau = (t2/s3) x s3 / t  =   t

which is now correct.

Revised 06/09/2012