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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
1 year, 7 months 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 - 1 year, 7 months ago

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

Swapnil Das - 1 year, 7 months ago

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

Pranshu Gaba - 1 year, 7 months 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 - 1 year, 7 months ago

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Comment deleted Apr 19, 2016

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@Rishabh Cool As per the book, probably yes. You may check out Fundamentals of Physics.

Swapnil Das - 1 year, 7 months ago

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Comment deleted Apr 19, 2016

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Comment deleted Apr 19, 2016

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

BTW, Thanks a lot!

Swapnil Das - 1 year, 7 months 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 - 1 year, 7 months ago

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@Pranshu Gaba Ok..I'll try to upload updated pic maybe later on..

Rishabh Cool - 1 year, 7 months ago

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@Rishabh Cool Of course. Thanks again for help.

Swapnil Das - 1 year, 7 months ago

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@Pranshu Gaba Yeah exactly. Thanks for your time.

Swapnil Das - 1 year, 7 months ago

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@Rishabh Cool Oh yeah!

Swapnil Das - 1 year, 7 months ago

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Comment deleted Apr 19, 2016

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@Rishabh Cool Oh yeah, you are absolutely correct :)

Swapnil Das - 1 year, 7 months ago

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

Nitesh Chaudhary - 1 year, 7 months ago

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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!

Pranshu Gaba - 1 year, 7 months ago

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Exactly! We would love to hear from him.

Swapnil Das - 1 year, 7 months ago

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Sounds really interesting. Can you show your work?

@Nitesh Chaudhary

Swapnil Das - 1 year, 7 months ago

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