Why does electrical charge concentrate at sharp points?
Here is the mathematical way of understanding:



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.