Why is the electric field strong in sharp points??

iampaul

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.