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QAIPM-2000-Ph-3024: NEET 2000 Physics - Class 12 AIPM-2000-Ph-3024 Solution: Electric field at centre O of semicircle of radius a having…
Electric field at centre O of semicircle of radius a having linear charge density given as
Multiple Choice Options
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Step-by-Step Verified Solution
Considering symmetric elements each of length dl at A and B, we note that electric fields perpendicular to PO are cancelled and those along PO are added. The electric field due to an element of length d l ( = a d _ ) along PO.
d E = 1 4 � _ 0 d q a 2 cos _ _
( _ d l = a d _ )
= 1 4 � _ 0 _ d l a 2 cos _ _
= 1 4 � _ 0 _ ( a d _ ) a 2 cos _ _ Net electric field at O
E = � _ � / 2 � / 2 d E
= 2 � O � / 2 1 4 � _ 0 _ ( a d _ ) a 2 cos _ _
= 2. 1 4 � _ 0 _ a [ sin _ _ ] o � / 2
= 2. 1 4 � _ 0 _ a .1 = _ 2 � _ 0 a