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Re: Confused by a derivation.



Michael,

Just a quick response on your comments to John D.

"I think Bernard's comment about adding fields, to which you responded
"alway
always always" add fields was really a mistated problem. Yes, the
superposition principle always holds for the electric field, so we can
always add all the fields from the contributing charges to find the net
field. The key word is "contributing." What Bernard was really saying was
both sides of charge on a finite-thickness insulating sheet with charge on
both sides will contribute to the electric field on one side of the sheet
(i.e. we use all charges when we apply the superposition principle in this
case)"

OK

"whereas only the near-side charges of the finite-thickness conductive
plate contribute to the field on one side of the plate when we apply the
superposition principle."

Here I disagree emphatically. Both the near-side and the far-side charges
contribute to the field on one side of the plate when applying the
superposition principle. In fact the a calculationg of the net E field
demands that you compute contributions from all sources once the
electro-static equilibrium regime has been established.

<snip>

"This strikes me both true and false. In the true sense... Literally we
only
consider the charge on the near side because the electric field from the far
side does not penetrate the conductor."

I disagree with this statement as well. Place a charge inside a spherical
conducting uncharged shell. The region of space outside of the shell is not
"shielded" from the electrical influences of the enclosed charge.
Superposition doesn't care if their is an insulating or conducting region
between the source point and the field point, as long as you include
(superpose) *all* contributions from *all* sources when calculating the net
E field (in electro-static equilibrium) And they all must be included.

When you think in these terms, you find that conductors don't such much
provide impenetrable barriers to E field, but rather provide a source of
non-zero charge density that provides electric field that superposes in a
"destructive" way with that of the sources (from which you are presumably
shielding regions of space, e.g. with a Faraday cage).


So, when we apply the superposition principle to the
conductive sheet, are
we summing the fields from the charges on both sides?

I say yes, you are literally summing the fields from both sides.

Joel Rauber