Cube of side ‘a’. Find net force on one of the charges due to the presence of ether charges.

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Solution

Charges 1, 3 and 7 are at a distance 'a'. Charges 2, 4, 6 are at a distance $^{'} \sqrt{2} a^{'}$
Charges 2, 4, 6 are at a distance $^{'} \sqrt{2} a^{'}$
Charge 5 is at a distance $\sqrt{3} a$
Express the force due to each of the charges in vector form (using coulomb’s law) and add them up to get resultant force.
$e . g ._{1} = \frac{k q^{2}}{a^{2}} (+^k),_{2} = (\frac{^i +^k}{\sqrt{2}}),_{3} = \frac{k q^{2}}{a^{2}}$ and so on.

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