What follows are ideas I have along with established concepts.
Electrostatics
The surface contour or curvature of a metallic solid defines its properties. This occurs with the surface layer of atoms. When it’s electrically neutral, then the contour shape doesn’t matter because all electric fields cancel locally with adjacent charges. However, when there’s excess charge, which can only exist at the surface, then the contour shape becomes a factor because the excess charges interact with each other all along the conductor’s surface through mutual repulsions, and the surface curvature influences or determines the nature of these interactions (Purcell, 27). The excess charge constitutes its own layer. So, the excess charge at the surface imposes properties on the conductor. A consequence of this is that the conductor gets divided up into wrap around layers like the layers of an onion, or at least there are two such layers, the layer of excess charge at the surface, and the interior layer of atoms adjacent to it, which is the outermost electrically neutral layer. The surface layer of excess charge acts or operates on this outermost neutral layer. Although the atoms in a metallic solid are arranged in rectangular planes and therefore make right angles with each other, the radially emanating nature of electric field lines along with the fact that with the excess charge, electric fields aren’t cancelled out locally, makes the atoms behave as if they were not at right angles with each other but instead slanted at acute and obtuse angles with respect to each other. That is, the excess surface charge imposes the curvy contour on the conductor.
Excess Positive Surface Charge
When copper metal is touched to zinc metal, then the more electronegative copper metal pulls electrons from the zinc metal thereby causing the zinc metal to have excess positive surface charge. The copper metal takes these electrons from the zinc metal’s formerly electrically neutral surface layer of atoms. So, with excess negative charge, an excess charge layer is created on top of the electrically neutral surface layer, and with excess positive charge, the electrically neutral surface layer itself becomes the excess charge layer while the adjacent interior layer becomes the outermost electrically neutral layer.
The electrons which are taken from the surface layer are the type which bind the surface layer atoms together with each other. These are actually at the perimeters of chambers. The only other type involved with the surface layer are the ones which bind or anchor the surface layer atoms to the first interior layer atoms. These are also at the perimeters of chambers. In fact, with close packing, all of the bonding locations are at the perimeters of chambers since each atom of one layer nestles into one of these gaps in the adjacent interior layer. So, if the electrons which bind a surface atom to its neighbors in the surface layer are taken, then the surface atom is only bound to another atom at its base, that being an atom of the first interior layer. This results in the electron density getting diluted throughout the entire surface layer of atoms since one of the priorities of the delocalized electrons is to maintain uniform electron density throughout the conductor. Since because with close packing, all of the bonding locations are at the perimeters of chambers, then when electrons are taken from the surface layer of atoms, this causes the atoms creating a gap to spread apart through mutual repulsions, thereby widening the gap. Although the excess positive charge is created by electrons being taken from the surface layer, it’s always the case that this is a tiny percentage of the total amount of surface layer electrons.
Concave Contours
With a concave situation and excess positive charge, besides the fact that in the interior of a conductor, excess charges would be surrounded on all sides in close quarters by atoms and would therefore be more confined, a reason that excess positive charge only resides on the surface is because since a more exterior layer has more matter in it than a more interior one, it has more space for excess charge to get spread out over, and excess charges want to get as far apart from each other as possible. This is represented by electric field lines which converge towards the center of the conductor from the surface. These electric field lines represent the direction of electron movement, inwards, and therefore aren’t the type which emanate from a charged particle. They associate multiple atoms in a more exterior layer of atoms with a single atom in the adjacent interior layer. More generally, they associate a greater number of atoms belonging to a more exterior layer with fewer atoms belonging to the adjacent interior layer. This is done by the more exterior atoms partly surrounding the single or multiple adjacent interior atom(s). This indicates that excess positive charge in the single or multiple more interior layer atom(s) can be spread out over or amongst all of the associated, more numerous, adjacent exterior atoms. An equivalent to excess positive charge spreading apart is that the delocalized electrons will preferentially neutralize more interior layers first since these have less matter and therefore are more affected by the loss or gain of the same number of electrons than more exterior layers are (Chabay, 725). That is, greater disequilibrium results from the loss and more disequilibrium is neutralized by the gain of the same number of electrons with a more interior layer than is the case with a more exterior layer. So, there’s more of an impact with an interior layer than with an exterior layer when the same number of electrons is lost or gained. Also, because it takes fewer electrons to neutralize a more interior layer which means that fewer electrons have to be mobilized, then this represents less of an energy cost. Therefore, more interior layers are given priority over more exterior layers. So, electrons spontaneously get taken from more exterior layers in order to neutralize more interior layers. This means that if there’s excess positive charge in the interior of a conductor, then the conductor will be neutralized starting from the center, which is synonymous with excess positive charge traveling from the center to the surface. Excess positive charge can only exist in the interior of a conductor if it’s sufficiently brief, that being the time it takes for delocalized electrons to move in and neutralize. This is due to the fact that electrons are so much less massive than cations and therefore move so much faster that before cations really have a chance to significantly repel apart from each other due to excess positive charge, the electrons have swooped in to remedy the situation.
When the concave surface is sharper or more pronounced, then the concentration or density of excess positive charge is greater than when it’s more flat. This is because when there’s a sharper curve, it swerves or veers away sooner from electric field lines traveling alongside it in their straight line paths. This means that the electric field lines of one charged particle traveling alongside the curve won’t be able to travel as far before they can no longer intersect or strike an adjacent or neighboring charged particle since the electric field lines will travel above or over, instead of into, the other charged particles sooner. Since delocalized electrons travel to alleviate like charge repulsions between cations by going in between them, when there are fewer of these like charge repulsions since the cations encounter each other by their electric fields less, then the electrons have fewer situations to have to deal with. That is, electrons get pulled up alongside and in between the cations. So, when the cations repel each other less, then the electrons don’t have to go up alongside them as much, but instead can more stay at the base of the excess charge layer where they can reinforce bonds holding the excess charge layer to the outermost neutral layer since these bonds are threatened by the tugging of the excess charge layer. The fact that each surface atom is anchored at its base, nestled into a cavity in the first interior layer, means that the excess positive charge surface atoms push away from each other and spread apart at their exterior sides but can’t do this at their base ends. So, the like charge repulsions are the most severe at the base sides, and therefore this is where the electrons preferentially go to neutralize.
When the surface is more flat, then a larger percentage of the electric field lines emanating from a charged particle strike an adjacent charged particle further from its base and closer to its top resulting in more like charge repulsions between adjacent cations closer to the exterior side of the surface layer of atoms than is the case with a more curvy situation. So, with a more flat contour, delocalized electrons go further from the base and closer to the surface of the excess charge layer, whereas with a more curvy surface, delocalized electrons retreat or contract more towards the base of the excess charge layer. This has the effect of causing the excess positive charge of a sharper curve to reach or extend out further away from counterbalancing opposite charges, electrons, than is the case with a more flat surface, and this is what constitutes the greater concentration or density of excess positive charge of a more curvy surface compared with a more flat one. This is because with a more pronounced curve, when an outside object approaches, its proximity to positive charges is much greater than it is to negative charges. So, it encounters excess positive charges much more than if the surface was more flat where the proximity of negative charges to the outside object would be more comparable to its proximity to positive charges.
When electrons are taken from either a concave surface or a flat one, then the remaining electrons adjust to this by mutually going more towards the base of the excess charge layer. With a concave situation, this is because uniformity of electron density needs to be maintained, and for the electron density to contract inwards where the surface layer atoms are closer together thereby making less space, helps with this. Also, there needs to be maintained a sufficient electron density concentration, a healthy concentration for the sake of bonding, and this is aided by the electron density contracting towards the base where there’s less space. However, the electron density isn’t as concentrated as before the electron removals occurred partly due to the tugging on electron density caused by the repulsions between the more upper parts of the excess charge surface layer. With a more flat surface, there’s still the general tendency of the remaining electrons descending somewhat towards the surface layer’s base. This is because no surface is devoid of curvature. There can be vast tracts of completely flat regions, but eventually you’ll reach curvature. At the curvature locations, the electron density contracts inwards, and for the sake of uniformity, this contracting only gradually diminishes, extending deep into flat regions.
Convex Contours
With a convex situation and excess positive charge, the surface layer is what actually has the least amount of matter in it. So, it’s the opposite of the concave scenario. Also, because a convex surface is like a bowl, then electric field lines emanating from each excess positive surface charge converge into other excess positive surface charges throughout the interior of the bowl, thereby increasing the disequilibrium. Electric field lines representing the movement of charged particles, electrons, and not actual electric field emanating from charged particles, converge towards the surface through the interior indicating that electrons are actually supposed to move towards the surface layer, not away from it. This is equivalent to excess positive charge moving away from the surface layer and into the interior of the conductor. There can’t be a convex surface without there also being a concave one elsewhere on the conductor. However, there can be a concave situation without there also being a convex situation. So, when electrons move towards the convex surface, they get taken from the concave part of the surface layer since this allows for the excess positive charges to get as far apart from each other as possible. This electron movement is equivalent to excess positive charge moving from the convex surface to the concave surface by traveling through the interior. As explained previously, excess positive charge can exist in the interior of a conductor if it’s sufficiently brief, that being the time it takes for delocalized electrons to rush in and neutralize.
Excess Negative Surface Charge
When the excess charge is negative, excess electrons, which is the situation with the copper metallic solid when copper metal is touched to zinc metal, then this resides on the exterior sides of the surface atoms, the sides which aren’t involved with bonding. Because there aren’t valence electrons here, the protons corresponding to this section of a surface atom aren’t getting enough electron coverage treatment. So, they welcome excess electrons to have this role. However, since there aren’t positive charges in this excess charge layer to keep electric fields locally cancelled out, the excess electrons repel each other all along the excess charge layer. This is as with a Van de Graaff generator. Eventually, the like charge repulsions between the excess electrons with each other becomes so great that it prevents any more extra electrons from being incorporated into the excess charge layer. Excess electrons can continue to be added as long as the attractions between them and the surface layer atoms are greater than their repulsions with each other in the excess negative charge layer.
Concave Contours
If the surface is concave, like a hill, then the sharper or more pronounced the curvature, the greater the density or concentration of the excess electrons. This is because electron electric field lines travel parallel to the conductor’s surface but can’t make it through the interior since there are opposite charges there which cancel with them, specifically the protons corresponding to the exterior sides of the surface atoms, which aren’t receiving adequate electron coverage treatment. So, the flatter the surface, the greater the distance that electron electric field lines can travel before the surface curves away, which means that they can repel other electrons on the surface for a greater distance. This is as with line of sight associated with someone trying to sneak up on someone else on a hill. The flatter the hill, the further away they can spot each other because the hill is less in the way, but the steeper the hill, the closer one individual can get to another before they spot each other.
Convex Contours
If the surface is convex, like with a valley, then the excess negative charge is very sparse in the bowl area due to electrons repelling each other. This is because there’s not the issue of electric field lines being blocked due to part of the conductor’s interior being in the way. This is analogous to people in a valley or along the rim of a crater being able to spot each other from a vast distance because there aren’t any mountain peaks or hills blocking their view. Most of the electrons go from the convex surface to the concave one, since there can’t be a convex surface without there also being a concave one. Although excess positive charge can travel through the interior since it’s propagated by the movement of electrons seeking to maintain electrical neutrality, excess electrons can’t travel through the interior because their repulsions with each other and their local environments wouldn’t allow for them to escape the interior fast enough.
Works Cited:
Purcell, Edward M., David J. Morin. Electricity and Magnetism, 3rd ed. Cambridge University Press, 2013.
Chabay, Ruth W., Bruce A Sherwood. Matter and Interactions, 4th ed. Wiley, 2015.