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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 $$\displaystyle \frac{Qa}{\pi \varepsilon_0 x^3}$$
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
$$E_{net}=2|E|=\dfrac{Qa}{\pi\epsilon_0x^3}$$

572784_222412_ans_78997935f39e418f8f73b9c8b1d4aa21.png

Physics
NCERT
Standard XII

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