Question 1.29 A
hollow charged conductor has a tiny hole cut into its surface. Show that the
electric field in the hole is (σ/2ε0) ˆn , where
ˆn is the unit vector in the outward normal direction, and σ is the
surface charge density near the hole.
Answer:
Method -1
Let us consider a conductor with a cavity or a hole. Electric field
inside the cavity is zero
Let E is the electric field just outside the
conductor, q is the electric charge,
According to Gauss’s law,
Therefore, the electric field just outside the conductor is 
These fields are equal and opposite inside the
conductor, and equal in magnitude and direction outside the conductor
Hence, proved.
Method -2
