# Charge on q from other charges given net force is zero

## Homework Statement

Consider the figure below, we need to find the charge on $Q_0$, both charges Q are negative. It is given that the net charge on $Q_A$ is zero.

The figure of the problem is attached.

## The Attempt at a Solution

I understand how to get the solution except for one part. I'm just going to write $F_x$ and $F_y$ below to denote the forces components as the numbers aren't relevant (I don't think?) for my question.

I understand that we can discard the constant $1/4\pi\epsilon_0$ or k whichever is preferred and that we can get rid of the $a^2$ terms in denominators when taking the radius and likewise for sin/cos for the respective components.

The solution is $Q_0 Q/8 = \sqrt {F_x^2 + F_y^2}$.

Now the solution is obtained by $Q_0 = 8 * \sqrt {F_x^2 + F_y^2}$

Why is Q discarded here? I just don't see where it goes mathematically.. it just kind of "disappears". Is it discarded because it is stated that the net force caused by this charge is negligible?

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haruspex
Homework Helper
Gold Member
It is given that the net charge on QA is zero.
That doesn't mean anything. Do you mean the net force on QA is zero, or the potential at QA is zero?

Please clarify what Fx and Fy represent.
I don't understand why you would have Q0Q in an equation. You don't care about any forces acting between Q0 and the two Q charges. Did you mean Q0QA?

The units on the solution aren't consistent. They show that (units of electric charge)^2 = force.

I didnt understand where the Q went until I reworked it and yes you're right. Is the below correct? It gives me the correct answer but as far as best way to solve technique etc goes not sure its close to good.

My notation could probably use some work... I realize I could have forgotten about the Q_0 components but split this up for practice breaking components up anyways.

I attached the work instead of trying to type tons of latex and mess it up

#### Attachments

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haruspex
Homework Helper
Gold Member
I didnt understand where the Q went until I reworked it and yes you're right. Is the below correct? It gives me the correct answer but as far as best way to solve technique etc goes not sure its close to good.

My notation could probably use some work... I realize I could have forgotten about the Q_0 components but split this up for practice breaking components up anyways.

I attached the work instead of trying to type tons of latex and mess it up
It's probably neater to use the symmetry. Just use the components parallel to the line x+y=0.

I'm not sure what you mean? I'm very bad at using symmetry doing these types of problems typically takes me ages as I can't identify the symmetry / relations correctly in square arrays of charge etc. Could you explain what you mean?

haruspex