σ is the charge per unit lenght. o is the actual centre of part of the spherical shell. to find the value of electric field at pt. b. this is the way how i proceed. i took a small part of shell of length dx. then took variable distt from b in form of x & θ. i integrate but could not relate between x & θ.& cant simplify in one variable. please help me out..
Your description and your diagram are confusing and don't seem to match each other very well. Please try to be more precise.
i took a part dx. then took electric field from b in terms of θ , β , x & took the sin component. replaced β in terms of x & θ by using cosine Δ formulae. but i could not relate x, θ & cant found the ans.
You need to show your work. That's the only way where we can see where you are getting off track. For instance, when you say "took the sin component", it isn't obvious which angle you are taking the sine of. Sure, I could take a guess. But what if the mistake you are making is that you are taking the sine of the wrong angle? Are you computing dx (which should probably be called dl or something other than x) correctly? Can't tell. Are you computing the angle β correctly? Can't tell. Show. Your. Work. Also, a better diagram would certainly help, especially since there appear to be English language issues, as well. Perhaps the attached diagram will help (thrown together in Paint in under five minutes -- so it doesn't have to be fancy or take a long time or use expensive software tools).