Six charges are placed at the vertices of a rectangular hexagon as shown in the figure. The electric field on the line passing through point O and perpendicular to the plane of the figure as a function of distance x from point O is (xgtgta)

Options

A. 0
B. `(Qa)/(pi epsilon_(0)x^(3))`
C. `(2Qa)/(pi epsilon_(0)x^(3))`
D. `(sqrt(3)Qa)/(piepsilon_(0)x^(3))`

Answer

b

Explanation

Two opposite charges situated at opposite vertices forms a dipole and point lies on bisector line of dipole for on dipole

`vec (E )= (-Kvec(P))/(x^(3))`
direction of field due to these three dipoles is in a horizontal plane at distance `x` from plane of hexagon and parallel to it, mutually having angle `60^(@)` with each other.
`E_(0)= E+E=2E= 2(Q(2a))/(4piepsilon_(0).x^(3))= (Qa)/(pi epsilon_(0)x^(3))`