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

#ElectricityAndMagnetism

Easy Math Editor

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Comments

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 years, 1 month ago

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

Swapnil Das - 5 years, 1 month ago

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

Pranshu Gaba - 5 years, 1 month ago

@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 years, 1 month ago

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

Nitesh Chaudhary - 5 years, 1 month 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!

Pranshu Gaba - 5 years, 1 month ago

Exactly! We would love to hear from him.

Swapnil Das - 5 years, 1 month ago

Sounds really interesting. Can you show your work?

@Nitesh Chaudhary

Swapnil Das - 5 years, 1 month ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$