A ring of charge with radius of 0.5 m has 0.02 m gap. if the ring carries a charge of +1C the field at the centre is

electric field at centre =electric field of ring without gap (this is equal to zero)+E'

now, what is E'? gap is small enough to be considered as a point charge. let us consider that the charge at the gap would have been q if there was no gap. now add a charge -q to that region. This produces the gap.We must use the principle of superposition. q=(0.02/(2pi*0.5))*(+1), -q=(0.02/(2pi*0.5))*(+1),field due to -q at centre=(-q/4piε₀)(0.5²) in the direction pointing at the gap.