A circular wire of radius R carries a total charge Q distributed uniformly over its circumference. A small length of wire subtending angle teta at the centre is cut off. Find the electric field at the centre due to the remaining portion

Answer 1

Treat the problem as the superposition of a complete loop of wire a nd a short length of negatively charged wire with the same absolute value of charge per length. The field at the center due to the complete loop is zero. Treat the negatively charged segment as a point source.