question_answer 29)

A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole iswhere is the unit vector in the outward normal direction, and  is the surface charge density near the hole.  

Answer:

Let the tiny hole of the conductor be considered as filled up. Field inside the conductor is zero whereas outside it is given by . This field is infact due to                 (i) field due to plugged hole                 (ii) field due to rest of the charged conductor.                 Inside the conductor these fields are equal but opposite whereas outside they, are exactly same.                  Electric field in the hole .