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Think of a metal object with one side round and the other side sharp.
And we charge the metal either negatively or positively.

Why is charge more concentrated at the sharp point?

Why Don't electrons repel each other stronger at sharp point? So that they go away from the sharp point?

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  • \$\begingroup\$ rub a glass bar against silk. then touch the glass to the metal. it is negatively charged now. if you want positive, use plastic bar and wool. \$\endgroup\$ – AHB Dec 9 '15 at 16:44
  • \$\begingroup\$ Pardon me. Isn't it better to ask your question here: physics.stackexchange.com \$\endgroup\$ – Roh Dec 9 '15 at 16:55
  • \$\begingroup\$ Corona occurs when conductor is grounded. Suspended conductor does not have any potential. Charges concentration becomes higher as the conductor cross section decreased. Same as electric current flow in conductors \$\endgroup\$ – GR Tech Dec 9 '15 at 16:57
  • \$\begingroup\$ @GRTech. my question is exactly why "Charges concentration becomes higher as the conductor cross section decreased" ? \$\endgroup\$ – AHB Dec 9 '15 at 17:03
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    \$\begingroup\$ @BlueSky In microscopic view, current has a standard "volume" (if electric field remains the same). So if you "squeeze" the current to a thinner conductor (smaller cross-section), the current density increased accordingly. \$\endgroup\$ – GR Tech Dec 9 '15 at 21:16
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Here is the mathematical way of understanding:

enter image description here

Now I'll try to explain it logically:

Consider a room full of people who don't want to see one another or be close to. If the room is symmetric (consider circle), they will try to keep uniform distance so that everyone is as far from one another as possible. Now add a narrow lane to the room so that only a line of people can be formed there. People will notice that if they go into the lane, they will have fewer people close to them (only 2, one in front and one in back) as compared to when they were in the circular room. This is a better configuration for those people.

However this will lead to increased number of people per unit space in that lane and a person looking from far will notice that even though they want to get away from one another, they have crammed up in same place.

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It's not more concentrated (as your gut is suggesting) but the electrical stress is higher at a point and if you're going to have a discharge it will happen at the point.

In layman's terms this effect is seen in many areas. Cracks or tears propagate easily - in paper, plastic or metal, for example. This would be familiar to anyone trying to tear off a piece of adhesive tape: it's very difficult if the edge is continuous. Make a nick in the tape and it's very easy to propagate the tear. I understand that cracks in metal aircraft skin can be stopped by drilling a hole at the end. The stress is now spread around the circumference of the hole. Use a paper punch on a sheet of paper and tear the paper into the hole. You should notice that it takes quite a lot more force to restart the tear out the other side of the hole.

The effect is most familiar to all of us in the form of a knife. A sharp knife creates very high stress in the material being cut if the edge is sharp. When it dulls the stress is spread around the circumference and cutting action is more dificult.

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    \$\begingroup\$ His gut suggestion is correct. Surface charge actually is more concentrated on sharper points (the charge density is proportional to the "stress." See other answers here for details. \$\endgroup\$ – wbeaty Jan 13 '17 at 19:00
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Short answer: The metal surface is at the same potential. The local electric field goes as one over the radius of curvature at that point. And the electric field is proportional to the local charge density. Net effect is that charges concentrate at sharp points. For more details study electrostatics.. it's all in Maxwell's equations.

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