a thin half ring of radius R=20cm is uniformly charged with a total charge q=0.70mC.find the magnitude of electric field strength at the centre of curvature of this half ring

hi sneha,

  charge per unit length, λ=total charge/half the circumference

after an angle @ cut an element of length rd@,

therefore,charge dq= λrd@

now elec field due to this element is dE=kdq/r²

the cos @ component of dE will be cancelled and sin @ component will add  up

therefore total elec field=2dEsin @

this expression can be integrated from @=0 to pi/2 to get the desired answer