__On
the Fields of a Spinning Disk of Charge __

Let us begin by modeling a
spiral galaxy as a disk of single-valued mass density s=m_{galaxy}/pR^{2}, lying in the xy-plane and
rotating with an angular velocity w that points in the +z
direction. In the article __Galaxies and the Gravitomagnetic Force__ it was
found that such a galaxy theoretically has an Imaginary uniform gravitomagnetic
field __O__ that points in the z direction:

O_{z} = 2pGswR/c^{2}.
(1)

=2G i|m_{galaxy}| w / Rc^{2}.

Given a star of mass i|m_{star}|,
momentarily on the x-axis and at a fixed distance r from the galaxy’s center,
the gravitomagnetic force on the star is then (according to the GMT version of
the Lorentz force law)

F_{gravmag x} = i|m_{star}|
(v_{y}O_{z}) (2)

= i|m_{star}| (wr)
O_{z}

And the total force on the star
is theoretically the sum of the gravitomagnetic force plus the gravitational
force (which also points toward the galactic center):

F_{total x} = F_{gravmag
x} + F_{grav x}.
(3)

Now Newton 2 indicates that F_{total x}
is:

F_{total x} = |m_{star}|
a_{ } (4)_{
}

_{
}= - |m_{star}| w^{2}r.

Assuming that

F_{grav x} = i|m_{star}|
g_{x}
(5)

where g_{x}
is the gravitational field of the galaxy at the star’s position, we find that

g_{x} = F_{grav
x} /i|m_{star}|
(6)

= (F_{total x} - F_{gravmag x}) / i|m_{star}|

= - |m_{star}| w^{2}r
+
(2Gi|m_{star}|)(i|m_{galaxy}| w^{2}r) / Rc^{2}) /i |m_{star}|.

=
i(w^{2}r -
2G|m_{galaxy}| w^{2}r / Rc^{2}).

Using the GMT rules that
(1) g/i transforms to E, (2) G transforms to 1/4pe_{o}, and (3) O transforms to
B, we find that, given a spinning disk of positive *charge*
with uniform charge density s, the electric field in the
disk’s plane points away from the center and has the magnitude

E_{ }=
w^{2}r+(qw^{2}r /2pe_{o} Rc^{2}). (7)

And, applying the same
transformations to Eq. 1, we find that

B_{z}=m_{o}swR/2.
(8)

Eq. 8 agrees with the value for B specified on the Internet.