Why is the electric field strong in sharp points?

[iampaul]

Why is the electric field strong in sharp points??

There is a question in my book regarding the intensity of the electric field near a sharp surface in a conductor. There is a hint which says that it will be helpful to examine the field lines near those sharp surfaces. This is from my University Physics book by young and freedman after a chapter about gauss law, and before the chapter about electric potential. Please reply. Thanks

 

[meldraft]

The divergence of the field becomes greater in sharp points. You can easily explain this intuitively if you think of it as a conformal map. As the geometry becomes sharper locally, the field lines come closer to each other, increasing the divergence of the field and thus, the local intensity.