A hollow sphere of radius a carries a total charge Q distributed uniformly over its surface. A small area dA of the sphere is cut off. Find the electric field at the center due to the remaining sphere.
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Sol.
Small part 'AB' of hollow sphere of area 'dA' is cut off. Now, electric field at center 'O' of system will only be due to part CD of area 'dA' directly in front of it. [rest is cancelled out]
Let charge on CD ⇒ dQ
∴ dQ = 
. (dA)
E O = Electric field at O i= 
= 
dA. 
∴ E O = 
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