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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 of 34
Marks: +1, -0
A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole is (σ2ε0)n^\left(\frac{\sigma}{2\varepsilon_0}\right) \hat{n} , where n^\hat{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 σ2ε0\frac{\sigma}{2\varepsilon_0} normal to its plane.
If we consider a small flat part on the surface of charged conductor, it certainly provides an electric field σ2ε0\frac{\sigma}{2\varepsilon_0} 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 σ2ε0n^\frac{\sigma}{2\varepsilon_0} \hat{n}
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