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13 Jul 2009 09:32:20 IST

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A semi-circular arc of radius a is charged.....

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A Semi-circular arc of radius a is charged uniformly and the charge per unit length isλ. What is the electric field at the centre?

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BALGANESH

Blazing goIITian

Joined: 21 Dec 2007

Posts: 1025

13 Jul 2009 09:54:05 IST

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consider a small portion of the arc

now let the small portion be dl

so charge dq= λdl

but dl = a d@ where @ is teh angle subtended by it at the cnetre

thus dq=λ a d@

dE=K dq/a^2 sin@ bcos the cos@ components gets cancelled due to symmetry

dE = K λa d@ / a^2 sin@

integrating both sides with limits 0 to E for E and 0 to pie for right hand side

E =K λ/a *[cos pie - cos 0]

= 2K λ / a

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