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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) :
222412_276f39282f014e0fb49a81e24640e95f.png

A
0
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B
Qaπε0x3
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C
2Qaπε0x3
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D
3Qaπε0x3
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Solution

The correct option is B Qaπε0x3
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=kpx3=Qa2πϵ0x3
Now three fields exists as shown in figure, so
Enet=2|E|=Qaπϵ0x3

572784_222412_ans_78997935f39e418f8f73b9c8b1d4aa21.png

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