At what distance along the central perpendicular axis of a uniformly charged plastic disk of radius 0.390 m is the magnitude of the electric field equal to one-half the magnitude of the field at the center of the surface of the disk?

Radius, the distance from the centre = 0.390

Electric field is equal to half of the magnitude. E2 = E / 2

Given

E1 = E2 E1 = k x Q / r^2

E2 = (k x Q / r2^2) / 2

Equating the both we get 2 x r^2 = r2^2

r2 = square root of (2 x r1^2) = square root of (2) x r = 1.414 x 0.390

r2 = 1.414 x 0.390 = 0.551 m