Question

# 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 (x > > a) :

A
0
B
Qaπε0x3
C
2Qaπε0x3
D
3Qaπε0x3

Solution

## The correct option is B $$\displaystyle \frac{Qa}{\pi \varepsilon_0 x^3}$$Consider any two charges opposite sides of O, they form a dipole where $$p=2Qa$$.Electric field due to dipole on it's axis is given by $$E=\dfrac{kp}{x^3}=\dfrac{Qa}{2\pi\epsilon_0x^3}$$Now three fields exists as shown in figure, so$$E_{net}=2|E|=\dfrac{Qa}{\pi\epsilon_0x^3}$$PhysicsNCERTStandard XII

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