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chomebole

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chomebole

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Meir Achuz

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There are various ways of doing this, depending on the exact situtation.

Then sigma=E/4pi at the surface (in gaussian units).

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arunma

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Meir Achuz

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For instance for a point charge q a distance d from an infinite plane, the E field can be found by using an image charge. Then using the E field at the surface of the plane, the surface charge is sigma=-qd/[r^2+_d^2]^{3/2}

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mdelisio

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In general, you know that the charges on the conductor are all going to reside on the surface. You also know that the potential at the conductor's surface (and inside its volume) must be constant. One application of the method of moments divides the surface up into many smaller subsurfaces, and assumes a constant charge density on each subsurface. You can then solve for the potential at, say, the center of any subsurface due to the charge at a single subsurface. Superposition also applies. You wind up with a matrix equation:

Vm = Lmn*qn (summing over the n's is implied)

Where Vm is the potential at subsurface m, qn is the charge density at subsurface n, and Lmn is the matrix connecting them. You invert this matrix to find the q's for constant V's. The accuracy depends on how finely you chop your surface up into.

It can be a very messy problem, especially for complex geometries, and requires a computer to help with the matrix inversions.

As a simple example, you might want to consider a thin square metal plate. Divide it up into, say, a 4x4 array of smaller metal squares. Solving this will show you that the charge tends to pile up in the corners.

- #6

arunma

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For instance for a point charge q a distance d from an infinite plane, the E field can be found by using an image charge. Then using the E field at the surface of the plane, the surface charge is sigma=-qd/[r^2+_d^2]^{3/2}

You're right, I completely forgot about this. I just checked my old E&M text (Griffiths), and found that he does this for the case of the infinite conducting sheet.

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vish_al210

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I have a small questio though., I understand that the charges on a conductor may//can vary along its length and periphery. But then when I consider a conductive wire, at what point do u think I can get a potential difference != 0, but a value... and if so for how long. By 'what point', i am referring to any segment or length of wire where a probe maybe placed.

Please a lot of my theory depends on it.

Please a lot of my theory depends on it.

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vish_al210

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Well how infinitely small can one assume this time to be if the conductor in question is any normal conductive, copper, Al wire... or any other conductor... is that a reasonably long duration for that potential change to affect the effective potential difference of the system. Thanks..During this time u can measure a potential difference.

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Well how infinitely small can one assume this time to be if the conductor in question is any normal conductive, copper, Al wire... or any other conductor... is that a reasonably long duration for that potential change to affect the effective potential difference of the system. Thanks..

This time is generally small and it depends on the size and on the conductance (reciprocal of resistivity) of the conductor. The smaller the size and the bigger the conductance, the smaller the time will be. If the conductor we talk about is part of an AC circuit you want this time to be small when it is compared to the period of the AC current/voltage.

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