circular wire loop of radius a A carries a total charge Q distributed uniformly over its length.A small length dL of the wire is cut off, find the electric field at the centre due to the remaining wire.

total charge=Q

charge per unit length=Q/2pia

charge contained by dL lenght of element = dq=QdL/2pia ...........1

now

     net electric field at the center of ring is E= 0 ....

when dL element is cut from the ring then let the field of remaining is E_R..

so we can say that total electric field at center = E_R + electric field due to dL element    

       (total electric field is vector sum of all components)

0=E_{R + k}dq/a²

  E_{R= -(KQdL/2pi}a³)