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Re: [Phys-L] circular definition of "success" .... was: standard DC circuits



The left plots are of electric potential as a function of two spatial dimensions, one of which is along the direction of the background field. The right plots are of charge density as a function of the same spatial dimensions. The only place there IS non-zero charge density is on the wire (and to some small extent, as an artifact of the numerical method, on the boundaries of the spatial region.) In each case the relaxation method is applied to a rectangular region whose boundary is held at a potential that enforces the uniform background field and within which lies a short "wire" aligned with the background field and held at V = 0

To be a little more specific:

In the first case the background potential runs from 25 to -25 so that the midpoint of the wire is at the same potential as that of the background field.

In the second case the background potential runs from 5 to -45 and in the third case the the background potential runs from -5 to -55

In each case the charge density throughout the region is obtained as the laplacian of the potential.

John Mallinckrodt
Cal Poly Pomona

On Dec 3, 2013, at 12:34 PM, Jeffrey Schnick wrote:

What is being plotted here? In particular what do the horizontal axes represent? Are we talking about a straight current-carrying wire whose ends are held at two constant values of potential for three different cases of the two values of potential? Is the entire apparatus placed in a region of space in which the electric field was uniform prior to the introduction of the wire and the circuit used to hold the ends at the two values of potential?

On November 30, John Mallinckrodt wrote:

The "grounding" part is potentially (pun virtually unavoidable) problematic
because we don't know HOW it is grounded, i.e., what OTHER conductors
might be involved. Better simply to say that we will ensure that it carries an
appropriate amount of charge to BE at whatever potential we are calling
"ground" potential. Then, all one needs to do is understand that the wire
WILL come to some constant potential along its length by distributing
whatever charge it has so as to accomplish that result. Clearly there will be
no field IN the wire because it's a conductor. You can quickly visualize what
the filed must look like simply by imagining a downward sloping sheet with a
linear section of it distorted into a constant horizontal level.

I made some images using a spreadsheet I put together long time ago to
solve Poisson's law problems using the relaxation method. You can look at
the results here.

https://dl.dropboxusercontent.com/u/409806/WireInUniformField.pdf

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