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nick (462)

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Olaaa!! Perrrfect answer. 74  [120 rates]

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lets consider an element whose charge is dq

dq= q/pi.r rd@ where @ is small angular displacement
r gets cancelled

now field due to small part is dE= dq/kr^2

now taking the components cos@ is cancelled by all the parts by symmetry
only sin@ will "add" up
hence
dEsin@=dq/kr^2 sin@=dEtotal

q/kpi.r^2 d@sin@
integrating from limits 0 to pi

we shall get
Etotal= 2q/pir^2.k here k=4pi.e' e'=epsilon

this is the ans..

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