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)

A
0
B
$\frac{Qa}{{πε}_{0} x^{3}}$
C
$\frac{2 Qa}{{πε}_{0} x^{3}}$
D
$\frac{\sqrt{3} Qa}{{πε}_{0} x^{3}}$

Solution:

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

$\vec{E} = \frac{- K \vec{p}}{x^{3}}$

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.

$E_{0} = E + E = 2 E = 2 \frac{Q (2 a)}{4 {πε}_{0} \cdot x^{3}} = \frac{Qa}{{πε}_{0} x^{3}}$

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)

Solution:

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