Physics - electrostatic exercise with 4 charges at the corners of a square

[Hanz_]

Homework Statement

A charge Q1 is fixed in each of the two opposite vertices of the square,
a Q2 charge is placed in each of the other two opposite vertices.
a) Express Q1 through Q2 if the resulting electrostatic
the force acting on each charge Q1 is zero.
b) There is such a value of Q2 for which the resultant electrostatic force would
acting on each of the four charges was zero? Can you explain it to me please

Relevant Equations

I do not understand the procedure of integrations/derivations from which a formula will be created according to which I will calculate.

 

[berkeman]

Welcome to PF, Hanz.

Is there a figure that is associated with this exercise? If so, can you scan it and use the "Attach files" link to upload it? I'm not sure I'm understanding the problem statement if the two Q1 have the same value and the two Q2 have the same value...

 

[berkeman]

After thinking about it more I think I see a solution for part (a). Start with the Q1 charges negative, and the Q2 charges positive, and draw them at the vertices of the square. Then draw the resultant force vectors due to the electrostatic charges, and think about what the values have to be to balance out the forces on the Q1 charges.

 

[kuruman]

In your drawing, $\vec F_{123}$ is the hypotenuse of a right triangle with right sides $\vec F_{12}$ and $\vec F_{13}$. What should the relation of $\vec F_{14}$ be to these for the net force on the charge in the upper left corner to be zero?

 

[haruspex]

In your diagram, you have an expression for $\vec F_{12}$ and one for $\vec F_{123}$. Can you combine them?
You have not written an expression for $\vec F_{14}$.

There are no integrations nor differentiations to be done.