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Find electric field at centre of cube ?

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a

$\frac{- 2 q}{4 π 3 \sqrt{3} ε_{0} a^{2}} [\hat{i} + \hat{j} + \hat{k}]$

b

$\frac{2 q}{π 3 \sqrt{3} ε_{0} a^{2}} [\hat{i} + \hat{j} + \hat{k}]$

c

$\frac{q}{π 3 \sqrt{3} ε_{0} a^{2}} [\hat{i} + \hat{j} + \hat{k}]$

d

$\frac{- q}{π 3 \sqrt{3} ε_{0} a^{2}} [\hat{i} + \hat{j} + \hat{k}]$

answer is A.

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Detailed Solution

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If we consider two point charges +q and –q at position of –q charge, then after interchanging –q charge with +q charge, net electric field at centre of cube is zero due to symmetry. Now remaining charges are –2q so net electric field at centre is $(\frac{- 2 kq}{3 a^{2}})$

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