Doubt in electrostatics

@JEE2020
@Sanjay_S
@Abhinav.08
@Seshank
@Aastik_Guru

pls help guys
ans is sigma/pi eplsilon
thanks

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image

Bro, this method should give the answer.

Firstly, midpoint is given so that there is no electric field along the axis of semi-cylindrical sheet. Now, we take diff. element at theta, and we can find the charge density on it (for this we’ll have to convert charge/area into charge/length which is standard). Now, electric field due to infinite wire gives E. We can take it’s components Ex and Ey, and then integrate. Integration of Ex from 0 to pi will be zero.

Integrating Ey will give the answer.

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I tried something, but didn’t get the answer you’ve given. Not sure where I went wrong.

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