I can't visualise how the component of $B$ field perpendicular to the arc's axis will be distributed for different current elements on the arc. 
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1$\begingroup$ Could you add a drawing, please? Or, could symmetry help you to simplify this to full 2π loop (in which case the problem is simple)? $\endgroup$– dominecfCommented Jun 11, 2021 at 11:30
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$\begingroup$ OK ............. $\endgroup$– ayush_rocksCommented Jun 11, 2021 at 14:54
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As your problem lies in visualising, I hope you find this diagram useful(I tried to keep the shabbiness to a minimum):
Each element on the y-z plane would have a corresponding element that cancels out the component of the magnetic field perpendicular to the x-axis. What shall remain is the field along the x-axis. I wish I were able to depict this in the figure, but I didn't, lest it is hard to understand.
answered Jun 11, 2021 at 11:40
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$\begingroup$ Thanks for replying ...in the image it looks like u drew wrong direction for B field... Tell me if i am wrong $\endgroup$ Commented Jun 11, 2021 at 14:57
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$\begingroup$ @ayush_rocks I don't think so. The bold blue lines show the field on the XY plane; the green ones show the field in the XZ plane. You can just imagine a straight line from the element to the point. This will give you the direction of the field. $\endgroup$ Commented Jun 11, 2021 at 16:15
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$\begingroup$ I attached the image of the arc i am talking about..if possible then please derive a result for B field at x $\endgroup$ Commented Jun 11, 2021 at 16:28
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$\begingroup$ The magnetic field of an element is perpendicular to the radius from the element to the point. Not along the radius. See Biot-Savart law. $\endgroup$– nasuCommented Jun 14, 2022 at 19:08