Charge distribution and Shape [closed]

I can't seem to understand why charge accumulates on the sharp points on a conductors surface. I've seen many solutions with math's but I don't understand them and I want a more intuitive explanation. Is it the electrons like charge that causes them to lie on the surface of a conductor as well as to concentrate on sharp points?

I've read that electrons move to the surface of the conductor, because if they were in the center, it would create an electric field that would move the charges to the surface. But why is this electric field created when electrons lie in the center.

• Is your question "why do electrons accumulate on the surface of a conductor?" or "why do electrons accumulate at sharp points on the surface of a conductor?" Commented Jul 1, 2022 at 9:55
• Mainly the sharp points. But I also want to understand why an electric field is created when charges are in the center of a conductor. Commented Jul 1, 2022 at 10:13
• If there is electric field inside a conductor, the charges would move, until they cancel this field. Note that only excess charge is on the surface of the conductor, not all charge. In EM101 this is called ideal conductor. Commented Jul 1, 2022 at 11:07
• I would recommend that you edit this question to focus one of the two questions ("why on the surface?" "why more on sharp points?") and ask the other one separately. Commented Jul 1, 2022 at 12:00

Excessive charge is subjective to the Coulomb force. This force is repelling for like-charged particles, such as a bunch of electrons. If exessive charge was to be gathered in the bulk of a conductor (a material inside which net charge has the ability to move), then these repulsive Coulomb forces would push each and every electron (or charged particle) as far as possible from the other. This means on the surface of the conductor and in particular in the edges, which are in essence the areas in the surface of the conductor that are located as far as possible from the bulk.

If anything is unclear, please let me know in the comments.

• So are these repulsive forces because of an electric field that is created, if charges were inside the conductor? I don't really understand where the electric field comes in. Like why is an electric field created when charges are in the center of a conductor? Commented Jul 1, 2022 at 21:08
• In the fictional senarion in which I would (by hand) put charges in the bulk, then yes, the electric field would be created from the interaction between the charges (i.e. Coulomb force). But in electrostatics we do not have such senarios, because this does not describe static situations. The electric field created when charges are in the centre of the conductor exists because when two or more charges are brought together, then each of them exerts a force to the other. This force gives rise to an electric field. Commented Jul 2, 2022 at 6:34
• I am not sure if this makes things clearer, because I am not sure yet of what you are asking. If this does not cover you, please write to me again Commented Jul 2, 2022 at 6:34

Same free electrical charges (e.g. for example negative charge electrons) in a medium like a conductor metal repel each other with the Coulomb force and get attracted to opposite charges when subjected to the triboelectric effect or an external applied electric field on air:

$$|F|=K \frac{\left|q_{1}\right|\left|q_{2}\right|}{r^{2}}$$

The combination of these two opposite forces makes the free negative charges to separate spatially from the positive charges in a conductor metal. Depending on the electrostatic source-cause applied, thus other charged object in contact (i.e. triboelectric effect) or polarity of external electric field applied, negative charges (free electrons) can accumulate on the surface of the metal conductor or positive charges. Positive charges in a metal conductor is actually the absence or sparsity of free electrons in a region of the metal conductor.

triboelectric effect charge separation image source credits

The separated charges in a metal conductor quickly reach electrostatic equilibrium, a condition established by charged conductors in which the excess charge has optimally distanced itself so as to reduce the total amount of repulsive forces. Meaning that the same polarity charges (+ or -) are spread as far as possible from each other on the surface of the conductor (no other place really to go) according the the number of charges and the surface area of the metal conductor. The more the surface for a given number of existing charges the more spread out they become due to the Coulomb force previously described.

So it is a natural consequence that if the metal object has sharp edges or spikes because the reduced surface area in that regions of the conductor the same polarity charges to be more densely packed and squeezed together. Therefore a stronger electric field in that regions:

metal conductor with sharp surface region image source credits

After the external source (i.e. cause) of electrostatic charging of the metal thus other charged object (i.e. usually a dielectric material) in contact or external applied electric field is removed, metal conductors are known not to keep their charge polarization because the electrons are free to move and quickly they discharge and become neutral as before.

$$Note:$$ To avoid any confusion. The supplied two images in this answer. The first image above, only one side of each of the two rectangular shaped objects are rubbed together (triboelectric effect) therefore an opposite polarity charge is accumulated at the opposite side of each object (see layer 1 and layer 2). In the second image above, the whole surface of the object (green) is rubbed and subjected to the triboelectric effect (i.e. for example rubbed with a cloth) and therefore also the whole surface, opposite to the first image case, of the object is charged with the same polarity (see positive excess charge on surface).

• Is there more electrons on a sharp point, or are electrons more densely packed? If there are more electrons how do you explain this? Commented Jul 1, 2022 at 21:14
• @DominicTorreto Per unit surface area, the same number of charges. That what electrostatic equilibrium does due to the Coulomb repulsion force. If now the surface is not uniform and has localized regions of sharp edges, spikes, the charges are forced by the medium to be more squeezed closer together thus more dense packed but the number of charges per unit area remain the same. If for example the uniform distribution is 1000 charges/cm^2 and you have a spike 2cm^2 in surface you still will have 2000 charges but because the narrow shape their are more close together thus a stronger field. Commented Jul 2, 2022 at 11:22