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A thin long strip whose cross-section is a semicircle carries a uniform surface charge of density s on its inner surface. Find the electric field at a point O located midway on its axis.

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Link of image: https://s3mn.mnimgs.com/img/shared/content_ck_images/ck_5af85df600713.png

This is how I tried it. I considered a semicircular strip as the infinitesmial element. Then the electric field in horizontal direction gets cancelled out by symmetry. Only the downward vertical electric field remains. Then I derived a result for the electric field at a point on the axis of a uniformly charged half ring and I have used it to integrate it along the entire strip. But I get the wrong answer every time. Is this the right mathematical reasoning to do this??Can someone solve this? Thanks

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  • $\begingroup$ If you do it well it is the right procedure. $\endgroup$
    – user65081
    Oct 31 '21 at 13:46
  • $\begingroup$ Is the right answer $E=\frac{\sigma}{\pi \epsilon_0}$? $\endgroup$ Oct 31 '21 at 15:46
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Divide your surface into thin strips (like straight lengths of wire). Find the field at (0) from each of those. Then find the vector sum.

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