🚀 go-pugleaf

epperson@adobe.com (Mark Epperson) writes:
>>>The sharp points produce enormous fields. 

>Does this mean the the D ions will be more concentrated at the tip? 

Actually, the more intense the external field around a conductive surface, the
fewer relative charged "sites" it has.

Since a conductive surface will always settle to an equilibrium (any location
on the surface must have the same electrical potential as any other location on
the surface else charge carriers will be induced to move to make it so) the
only way for the conductive surface effect to accomplish such an equilibrium
is for charge carriers to tend to vacate any area of higher (non-uniform)
external electrical potential.  i.e. the relative scarcity of regional
charges makes up for and nullifies the stronger adjacent external field --
bringing the surface potential to be equal at all locations simultaneously.

You will actually find the highest density of charge carriers adjacent to
the portion of the surface with the lowest external field gradient.

In simple terms, similar polarity charges repel, hence where there is a high
concentration of similar polarity fields, mobile charge carriers will vacate
the area until a new equilibrium is established.


There are four general cases of conductive surface shapes, the point, the
wire, the plane, and the sphere.

The "point charge" gradient diminishes proportional to the inverse square of
the seperation.  Since at any non-infinitely small distance, this defines
a spherical space, the gradient around a sphere also diminishes proportional
to the inverse square of the seperation (measured from the center of the
sphere) for all locations on or beyond the surface.

The wire surrounding gradient dimishes more slowly with seperation (where
seperation is much less than wire length) because each charge along the
wire adds to the field at any given point.  Those points more distant have
less effect, but are also more numerous.  Seperation from points nearby
on the wire can quickly double or triple the distance from nearby charges,
but only change the the distance to the far more numerous more distant
charges by a tiny increment.

The result is that in the earths atmosphere, a sphere of about 15" in diameter
is require to hold a voltage potential of 1,000,000 volts without causing
electrical breakdown in the air due to high near surface gradients, while
it only requires a wire of about 2" in diameter to transport 1,000,000 volts
along a high tension power grid with causing electrical breakdown of the air.

The final general case is the flat plane, a two dimensional extension of the
one dimensional wire case.  The field gradient diminishes most slowly with
seperation in this case (where again, seperation is much less than the plane's
dimensions.)  Here the vector sum of many more charges are combined to produce
the field at any give point.  Hence seperation chances near the surface are
but a tiny increment in vector distance for most of the charges on the surface
of the plane and therefore the gradient diminishes very slowly with distance
(in the case of an infinite plane, there would be no voltage gradient at all.)

 
-- 
- John Logajan MS010, Network Systems; 7600 Boone Ave; Brooklyn Park, MN 55428
- logajan@network.com, 612-424-4888, Fax 612-424-2853