[EMAIL PROTECTED] wrote:
In polar coordinates the field has only a single value at a given
distance.
That's not correct. In polar coordinates the field is described by
three values at every point: the magnitude, and the altitude and
azimuth of the direction. If the charge is located at the origin, the
latter two will happen to match the alt and azi of the observer. But
that doesn't mean they're not needed to describe the field; it just
means you can mentally refer to them to the coords of the location and
not bother to write them down. If the point doesn't happen to be
located at the horizon, then none of the three parameters describing the
field will match the coordinates of the observer and it's harder to
forget to write them down :-)
To put it another way, if you use the (non-coordinate) unit basis
vectors (R, Theta, Phi), you can describe the field as
(k/r^2) * R
where R is the unit radius vector, and it _looks_ like there's just one
parameter. But that's not correct. First, to describe the basis vector
"R" you need three parameters (because it varies depending on the
location); and second, there are really three params here, but as an
artifact of the way you've chosen the coordinates the other two happen
to be zero. You've really got
(k/r^2) * R + 0 * Theta + 0 * Phi
Again, move the charge off the origin and those zeros change to messy
functions of the position.
Also, the permeability of space does not apply to the static
point charge.
I'm not following you. The permeability of space, which is arguably an
artifict of the units chosen (since it pretty much disappears in cgs
units), shows up in Maxwell's equations but isn't interesting unless the
fields are changing. But I don't see how that relates to the electric
field viewed as a scalar field?
Granted, a truly static point charge is purely a mental
construct; however, maybe you can see my point. <g>
Of course this thought experiment violates HUP since the proton is *not*
in motion.
-----Original Message-----
From: Stephen A. Lawrence
The E field is not a scalar field. A scalar field is represented by a
single number (magnitude) at each point; the E field is represented by a
vector at each point (magnitude _and_ direction -- that requires 3
numbers in 3-space, or 4 numbers in 4-space).
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