a thin conducting ring of radius R has linear charge density ?=?'cosa where ?'is a constant and a is the azimuthal angle. find the magnitude of the electric field strenght at the centre of the ring

hi sneha,

 after an angle a cut an element of length rda,so charge dq=?'cosa*rda

elec field due to this elemet ,dE=kdq/r² 

now consider another element of length rda at an angle -a,the magnitude dE due to both these elements is same

and therefore total elec field=2dE cosa in -x direction,sina components in +y dir.wll cancel out

so ,elec field at centre,E can be found by integrating this expression fron a=0 to pi and the elec field will be in -x direction.