# 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
2 years, 3 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?

- 2 years, 3 months ago

- 2 years, 3 months ago

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

- 2 years, 3 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.

- 2 years, 3 months ago

Comment deleted Apr 19, 2016

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

- 2 years, 3 months ago

Comment deleted Apr 19, 2016

Comment deleted Apr 19, 2016

Comment deleted Apr 19, 2016

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

BTW, Thanks a lot!

- 2 years, 3 months ago

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

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

- 2 years, 3 months ago

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

- 2 years, 3 months ago

Of course. Thanks again for help.

- 2 years, 3 months ago

Yeah exactly. Thanks for your time.

- 2 years, 3 months ago

Oh yeah!

- 2 years, 3 months ago

Comment deleted Apr 19, 2016

Oh yeah, you are absolutely correct :)

- 2 years, 3 months ago

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

- 2 years, 3 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!

- 2 years, 3 months ago

Exactly! We would love to hear from him.

- 2 years, 3 months ago

Sounds really interesting. Can you show your work?

- 2 years, 3 months ago