question: Why do electric charges tend to accumulate on the sharp points of a conductor?
comment: They don't accumulate there. They do have a greater chance of forming an arc or a corona there. That is due to the increased electric field (potential gradient) around a small point vs a plane. It is sort of like how a needle or knife can cut you, but a plate won't.
passages: The widely encountered phenomenon of electrical contact resistance or ECR, arises as an electric current flowing through a rough interface is restricted to a limited number of contact spots. The size and distribution of these contact spots is governed by the topological structures of the contacting surfaces forming the electrical contact. In particular, for surfaces with high fractal dimension contact spots may be very small. In such cases, when the radius of the contact spot is smaller than the mean free path of electrons formula_21 , the resistance is dominated by the Sharvin mechanism, in which electrons travel ballistically through these micro-contacts with resistance that can be described by the following 
   Section::::Formula.
  
  The AC current density "J" in a conductor decreases exponentially from its value at the surface "J"
  
  according to the depth "d" from the surface, as follows:
   While lower voltages do not, in general, jump a gap that is present before the voltage is applied, interrupting an existing current flow with a gap often produces a low-voltage spark or arc. As the contacts are separated, a few small points of contact become the last to separate. The current becomes constricted to these small "hot spots", causing them to become incandescent, so that they emit electrons (through thermionic emission). Even a small 9 V battery can spark noticeably by this mechanism in a darkened room. The ionized air and metal vapour (from the contacts) form plasma, which temporarily bridges the widening gap. If the power supply and load allow sufficient current to flow, a self-sustaining arc may form. Once formed, an arc may be extended to a significant length before breaking the circuit. Attempting to open an inductive circuit often forms an arc, since the inductance provides a high-voltage pulse whenever the current is interrupted. AC systems make sustained arcing somewhat less likely, since the current returns to zero twice per cycle. The arc is extinguished every time the current goes through a zero crossing, and must reignite during the next half-cycle to maintain the arc.
   The field strength is greatly affected by nearby conducting objects, and it is particularly intense when it is forced to curve around sharply pointed objects. This principle is exploited in the lightning conductor, the sharp spike of which acts to encourage the lightning stroke to develop there, rather than to the building it serves to protect
  
  Section::::Concepts.:Electric potential.
   Electric potential is a scalar quantity, that is, it has only magnitude and not direction. It may be viewed as analogous to height: just as a released object will fall through a difference in heights caused by a gravitational field, so a charge will 'fall' across the voltage caused by an electric field. As relief maps show contour lines marking points of equal height, a set of lines marking points of equal potential (known as equipotentials) may be drawn around an electrostatically charged object. The equipotentials cross all lines of force at right angles. They must also lie parallel to a conductor's surface, otherwise this would produce a force that will move the charge carriers to even the potential of the surface.
   A changing magnetic field will influence the distribution of an electric current flowing within an electrical conductor, by electromagnetic induction. When an alternating current (AC) flows through a conductor, it creates an associated alternating magnetic field around it. The alternating magnetic field induces eddy currents in adjacent conductors, altering the overall distribution of current flowing through them. The result is that the current is concentrated in the areas of the conductor farthest away from nearby conductors carrying current in the same direction.
   However, in very poor conductors, at sufficiently high frequencies,
  
  the factor under the large radical increases. At frequencies much higher than formula_15 it can be shown that the skin depth, rather than continuing to decrease, approaches an asymptotic value:
   Another situation this formula is not exact for is with alternating current (AC), because the skin effect inhibits current flow near the center of the conductor. Then, the "geometrical" cross-section is different from the "effective" cross-section in which current actually flows, so the resistance is higher than expected. Similarly, if two conductors are near each other carrying AC current, their resistances increase due to the proximity effect. At commercial power frequency, these effects are significant for large conductors carrying large currents, such as busbars in an electrical substation, or large power cables carrying more than a few hundred amperes.
   Often the contact region is heavily doped to ensure the type of contact wanted. As a rule, ohmic contacts on semiconductors form more easily when the semiconductor is highly doped nearby the junction; a high doping narrows the depletion region at the interface and allow electrons to flow in both directions easily at any bias by tunneling through the barrier.
   Proximity effect (electromagnetism)
  
  In a conductor carrying alternating current, if currents are flowing through one or more other nearby conductors, such as within a closely wound coil of wire, the distribution of current within the first conductor will be constrained to smaller regions. The resulting current crowding is termed the proximity effect. This crowding gives an increase in the effective resistance of the circuit, which increases with frequency.
  
  Section::::Explanation.
   where "R" = |r - r|, i.e. the distance from the area-element "da" to a particular point r on conductor i. σ is not, in general, uniformly distributed across the surface. Let us introduce the factor "f" that describes how the actual charge density differs from the average and itself on a position on the surface of the "j"-th conductor:
  
  or
  
  Then,
  
  can be written in the form
  
  i.e.
  
  Section::::Example.
  
  In this example, we employ the method of coefficients of potential to determine the capacitance on a two-conductor system.
  
  For a two-conductor system, the system of linear equations is
   The charge motion in a surface plasmon always creates electromagnetic fields outside (as well as inside) the metal. The "total" excitation, including both the charge motion and associated electromagnetic field, is called either a surface plasmon polariton at a planar interface, or a localized surface plasmon for the closed surface of a small particle.
   Similarly, in two adjacent conductors carrying alternating currents flowing in opposite directions, such as are found in power cables and pairs of bus bars, the current in each conductor is concentrated into a strip on the side facing the other conductor.
  
  Section::::Effects.
  
  The additional resistance increases power losses which, in power circuits, can generate undesirable heating. Proximity and skin effect significantly complicate the design of efficient transformers and inductors operating at high frequencies, used for example in switched-mode power supplies.
   The potential at any point in space, due to these two point charges of charge +"q" at +"a" and -"q" at -"a" on the "z"-axis, is given in cylindrical coordinates as
  
  The surface charge on the grounded plane is therefore given by
  
  In addition, the "total" charge induced on the conducting plane will be the integral of the charge density over the entire plane, so:
  
  The total charge induced on the plane turns out to be simply "–q".
   When the metal terminal is touched with a charged object, the gold leaves spread apart in an inverted 'V'. This is because some of the charge on the object is conducted through the terminal and metal rod to the leaves. Since they receive the same sign charge they repel each other and thus diverge. If the terminal is grounded by touching it with a finger, the charge is transferred through the human body into the earth and the gold leaves close together.
   BULLET::::1. "The electric field is zero inside a conductor." This is because charges are free to move and thus when they are disturbed by a field due to some external (or internal charge), they rearrange themselves such that the field that their configuration produces exactly cancels that caused by the source charge.
  
  BULLET::::2. "The electric potential is the same everywhere inside the conductor and is constant across the surface of the conductor." This follows from the first statement because the field is zero everywhere inside the conductor and therefore the potential is not changing with distance inside the conductor.
   BULLET::::- Contact electrification: If two conducting surfaces are moved relative to each other, and there is potential difference in the space between them, then an electric current will be driven. This is because the surface charge on a conductor depends on the magnitude of the electric field, which in turn depends on the distance between the surfaces. The externally observed electrical effects are largest when the conductors are separated by the smallest distance without touching (once brought into contact, the charge will instead flow internally through the junction between the conductors). Since two conductors in equilibrium can have a built-in potential difference due to work function differences, this means that bringing dissimilar conductors into contact, or pulling them apart, will drive electric currents. These contact currents can damage sensitive microelectronic circuitry and occur even when the conductors would be grounded in the absence of motion.
   BULLET::::- Free electrons at the cathode surface are created by the impacting ions. The problem is that the number of thereby created electrons strongly depends on the material of the cathode, its surface (roughness, impurities) and the environmental conditions (temperature, humidity etc.). The experimental, reproducible determination of the factor formula_35 is therefore nearly impossible.
  
  BULLET::::- The electrical field is homogeneous.
  
  Section::::Effects with different gases.
   In high current situations where conductors (round or flat busbar) may be between 5 and 50 mm thick the skin effect also occurs at sharp bends where the metal is compressed inside the bend and stretched outside the bend. The shorter path at the inner surface results in a lower resistance, which causes most of the current to be concentrated close to the inner bend surface. This will cause an increase in temperature rise in that region compared with the straight (unbent) area of the same conductor. A similar skin effect occurs at the corners of rectangular conductors (viewed in cross-section), where the magnetic field is more concentrated at the corners than in the sides. This results in superior performance (i.e. higher current with lower temperature rise) from wide thin conductors – e.g. "ribbon" conductors, where the effects from corners is effectively eliminated.
   in 1887 that the incidence of ultra-violet light on a spark gap facilitated the passage of the spark, led immediately to a series of investigations by Hallwachs, Hoor, Righi and Stoletow on the effect of light, and especially of ultra-violet light, on charged bodies. It was proved by these investigations that a newly cleaned surface of zinc, if charged with negative electricity, rapidly loses this charge however small it may be when ultra-violet light falls upon the surface; while if the surface is uncharged to begin with, it acquires a positive charge when exposed to the light, the negative electrification going out into the gas by which the metal is surrounded; this positive electrification can be much increased by directing a strong airblast against the surface. If however the zinc surface is positively electrified it suffers no loss of charge when exposed to the light: this result has been questioned, but a very careful examination of the phenomenon by Elster and Geitel has shown that the loss observed under certain circumstances is due to the discharge by the light reflected from the zinc surface of negative electrification on neighbouring conductors induced by the positive charge, the negative electricity under the influence of the electric field moving up to the positively electrified surface.
   However, in overhead transmission work on or near high-voltage lines, safety rules require connecting a conductor to earth ground during maintenance, since induced voltages and currents on a conductor may be sufficient to cause electrocution or serious injury.
  
  Section::::Origins.:Capacitive leakage through insulation.
  
  Alternating current is different from direct current in that the current can flow through what would ordinarily seem to be a physical barrier. In a series circuit, a capacitor blocks direct current but passes alternating current.
   As the skin effect increases, the currents are concentrated near the outside of the inner conductor ("r"="a") and the inside of the shield ("r"="b"). Since there is essentially no current deeper in the inner conductor, there is no magnetic field beneath the surface of the inner conductor. Since the current in the inner conductor is balanced by the opposite current flowing on the inside of the outer conductor, there is no remaining magnetic field in the outer conductor itself where formula_60. Only formula_67 contributes to the electrical inductance at these higher frequencies.
   Refer to the diagram below showing the inner and outer conductors of a coaxial cable. Since the skin effect causes a current at high frequencies to flow mainly at the surface of a conductor, it can be seen that this will reduce the magnetic field "inside" the wire, that is, beneath the depth at which the bulk of the current flows. It can be shown that this will have a minor effect on the self-inductance of the wire itself; see Skilling or Hayt for a mathematical treatment of this phenomenon.
   In an ideal conductor, where atoms are arranged in a perfect lattice structure, the electrons moving through it would experience no collisions and electromigration would not occur. In real conductors, defects in the lattice structure and the random thermal vibration of the atoms about their positions causes electrons to collide with the atoms and scatter, which is the source of electrical resistance (at least in metals; see electrical conduction). Normally, the amount of momentum imparted by the relatively low-mass electrons is not enough to permanently displace the atoms. However, in high-power situations (such as with the increasing current draw and decreasing wire sizes in modern VLSI microprocessors), if many electrons bombard the atoms with enough force to become significant, this will accelerate the process of electromigration by causing the atoms of the conductor to vibrate further from their ideal lattice positions, increasing the amount of electron scattering. High current density increases the number of electrons scattering against the atoms of the conductor, and hence the speed at which those atoms are displaced.
   Surface charge density is defined as the amount of electric charge, q, that is present on a surface of given area, A:
  
  formula_1
  
  Section::::Density.:Conductors.
  
  According to Gauss’s law, a conductor at equilibrium carrying an applied current has no charge on its interior. Instead, the entirety of the charge of the conductor resides on the surface, and can be expressed by the equation:
  
  formula_2
  
presuppositions: Electric charges tend to accumulate on the sharp points of a conductor.
corrections: Electric charges don't accumulate on the sharp points of a conductor, they form an arc on the sharp points of a conductor.
raw_presuppositions: Electric charges tend to accumulate on the sharp points of a conductor. Electric charges tend to accumulate on the sharp points of a conductor.
raw_corrections: Electric charges don't accumulate on the sharp points of a conductor, they form an arc on the sharp points of a conductor. Electric charges form an arc on the sharp points of a conductor.