# 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?

Swapnil

Note by Swapnil Das
3 years, 11 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?

- 3 years, 11 months ago

- 3 years, 11 months ago

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

- 3 years, 11 months ago

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.

- 3 years, 11 months ago

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

- 3 years, 11 months ago

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!

- 3 years, 11 months ago

Exactly! We would love to hear from him.

- 3 years, 11 months ago

Sounds really interesting. Can you show your work?

- 3 years, 11 months ago