how to find the electric field at a point x above the axis of a uniformly charged semi circular ring?

Question

how to find the electric field at a point x above the axis of a uniformly charged  semi circular ring?

masumanwar · Answer

what ever charge you can find at any finite distance using coulombs law

anonymous · Answer

i know that too but the problem in 3D becomes a bit confusing

anonymous · Answer

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anonymous · Answer

dq = Q/2piR

anonymous · Answer

kdq/r^2  =  kQ/2piR  *{  cos(theta) = z/(sqrt(z^2+R^2)) }  * 1/(z^2+R^2)

integrate all around the loop:
kQ/(2piR)  * (z/ (z^2 +R^2)^(3/2)) ds

=kQ/(2piR)  * (z/ (z^2 +R^2)^(3/2))  * 2piR

anonymous · Answer

there are 3 components of EF in space ,for a full ring two gets cancelled but for a half ring i think only one gets cancelled
is it true?

anonymous · Answer

ah half ring?  I didn't see that part..

anonymous · Answer

can you still help?

anonymous · Answer

you'll notice that one of the coordinate components of the field still cancels...so for instance..
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