Four charged particles are placed on the vertices of a square. The charges are \(+Q\)(depicted by green) and \(+q\)(depicted by blue). What should be \(\frac{Q}{q}\) so that both the particles having charge \(+Q\) experience net zero electrostatic force?

Please help me with this question. Thanks.

*Swapnil*

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## Comments

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TopNewestHave you tried drawing a free body diagram of the +Q charge?

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Oh yeah. I am stuck somewhere, in the calculations perhaps. Please help.

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Kindly share your progress with this problem. What forces did you get on the +Q charge?

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@Pranshu Gaba

I think it is correct. What do you thinkBTW, Thanks a lot!

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\[\frac{kQ^2}{2a^2} + \sqrt{2}\frac{k Qq}{a^2} = 0\implies \frac{Q}{q} = \boxed{-2\sqrt{2}}\]

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This can be easily done using physical form of Nash Equilibrium for charges.

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Wow! I have only encountered Nash Equilibrium in Game theory. I am interested to see how it can be applied in physics. Could you please elaborate on it? Thanks!

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Exactly! We would love to hear from him.

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Sounds really interesting. Can you show your work?

@Nitesh Chaudhary

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