First slide
Electric field
Question

Six charges are placed at the vertices of a regular 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 (assume x >>a)

Moderate
Solution

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

E=Kpx3

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.

E0=E+E=2E=2Q(2a)4πε0x3=Qaπε0x3

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