Two semicircular rings lying in the same plane of uniform linear charge density λ have radii r and 2r. They are joined using two straight uniformly charged wires of linear charge density λ and length r as shown in the figure. The magnitude of electric field at common center of semi-circular rings is

The electric field due to both straight wires shall cancel at common center O. The electric field due to larger and smaller semi-circular rings at O be E and E' respectively.At center of Arc : E=2kλrsinϕ2 For semicircle, take ϕ=π ⇒E=2kλrDue to Larger Semicircular ring : E=14πεo2λ2r Due to Larger Semicircular ring : E'=14πεo2λr∴Magnitude of electric field at O is⇒Enet=14πεo2λr−λr=14πεoλr