Consider *n* equal positive charged particles each of magnitude *Q*/*n* placed symmetrically around a circle of radius *a*. (a) Calculate the magnitude of the electric field at a point a distance *x* from the center of the circle and on the line passing through the center and perpendicular to the plane of the circle. (Use any variable or symbol stated above along with the following as necessary: *k _{e}*.)

*E*=

(b) Now consider a ring of radius

*a*that carries a uniformly distributed positive total charge

*Q*. Recall the calculation of the electric field at point a point a distance

*x*from the center of the ring and on the line passing through the center and perpendicular to the plane of the ring. Explain why the result in part (a) is identical to the result for the ring.