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A problem on Coulomb's Law

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

Note by Swapnil Das
5 months, 1 week ago

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  • Do you know the expression for Coulomb's law, which helps us find the electrostatic force between two point charges?

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

Pranshu Gaba · 5 months, 1 week ago

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@Pranshu Gaba Oh yeah. I am stuck somewhere, in the calculations perhaps. Please help. Swapnil Das · 5 months, 1 week ago

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@Swapnil Das Kindly share your progress with this problem. What forces did you get on the +Q charge? Pranshu Gaba · 5 months, 1 week ago

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@Pranshu Gaba All. I simply applied Vector form of Coulomb's law and plugged values. I did that for both the +Q charges and tried to equate. Doesn't seem to give nice results. Swapnil Das · 5 months, 1 week ago

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@Rishabh Cool As per the book, probably yes. You may check out Fundamentals of Physics. Swapnil Das · 5 months, 1 week ago

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@Rishabh Cool I think it is correct. What do you think @Pranshu Gaba

BTW, Thanks a lot! Swapnil Das · 5 months, 1 week ago

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@Swapnil Das Yup, the final answer's correct. However the equation before that is not correct; a minus (-) sign is missing. This is because the direction of the forces between Q and q is not correct. The force between +Q and +q would be repulsive and therefore the force on +Q will be up and left, and not down and right. The correct equation is

\[\frac{kQ^2}{2a^2} + \sqrt{2}\frac{k Qq}{a^2} = 0\implies \frac{Q}{q} = \boxed{-2\sqrt{2}}\] Pranshu Gaba · 5 months, 1 week ago

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@Pranshu Gaba Ok..I'll try to upload updated pic maybe later on.. Rishabh Cool · 5 months, 1 week ago

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@Rishabh Cool Of course. Thanks again for help. Swapnil Das · 5 months, 1 week ago

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@Pranshu Gaba Yeah exactly. Thanks for your time. Swapnil Das · 5 months, 1 week ago

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@Rishabh Cool Oh yeah! Swapnil Das · 5 months, 1 week ago

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@Rishabh Cool Oh yeah, you are absolutely correct :) Swapnil Das · 5 months, 1 week ago

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This can be easily done using physical form of Nash Equilibrium for charges. Nitesh Chaudhary · 5 months, 1 week ago

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@Nitesh Chaudhary 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! Pranshu Gaba · 5 months, 1 week ago

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@Pranshu Gaba Exactly! We would love to hear from him. Swapnil Das · 5 months, 1 week ago

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@Nitesh Chaudhary Sounds really interesting. Can you show your work?

@Nitesh Chaudhary Swapnil Das · 5 months, 1 week ago

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