# How do I find the electric field at the middle point in a thin long strip whose cross section is a semicircle?

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.

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

• If you do it well it is the right procedure.
– user65081
Oct 31 '21 at 13:46
• Is the right answer $E=\frac{\sigma}{\pi \epsilon_0}$? Oct 31 '21 at 15:46