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NCERT Class XII Chapter
Electric Charges and Fields
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Electric Charges and Fields

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Question : 29
Total: 34
A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole is (
σ
2ε0
)
^
n
 , where
^
n
 is the unit vector in the outward normal direction, and σ is the surface charge density near the hole.
Solution:  
Inside a charged conductor, the electric field is zero.

But a uniformly charged flat surface provide an electric field
σ
2ε0
 normal to its plane.

If we consider a small flat part on the surface of charged conductor, it certainly provides an electric field
σ
2ε0
 inside the conductor, which is nullified by an equal field due to rest of charged conductor.

Now if a hole is made in charged conductor, the field due to small flat part is absent but the field due to rest of charged conductor is present i.e., equal to
σ
2ε0
^
n
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