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

• Physics2341313
In summary: There is no symmetry in the figure. I think the best way to solve this is to use the symmetry of the line x+y=0.
Physics2341313

## 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?

#### Attachments

• P079afigure.png
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Last edited:
Physics2341313 said:
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

• work.png
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Physics2341313 said:
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?

Physics2341313 said:
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?
Where could you put a straight line through the diagram so that the portions on eithe side are mirror images of each other? Hint: two of the charges are unique, so it must pass through each of those.

## What does the term "net force is zero" mean in regards to charges?

The term "net force is zero" means that the total force exerted on a charged particle by other charges is equal to zero. This can occur when the forces from different charges cancel each other out.

## How does the charge on a particle affect the net force?

The charge on a particle can affect the net force by either attracting or repelling other charges. Like charges (positive and positive, or negative and negative) will repel each other, while opposite charges (positive and negative) will attract each other.

## What is the relationship between the distance between charges and the net force?

The net force between charges is inversely proportional to the square of the distance between them. This means that as the distance between charges increases, the net force between them decreases.

## How can you calculate the charge on a particle from the net force being zero?

To calculate the charge on a particle from the net force being zero, you can use Coulomb's Law. This law states that the force between two charges is equal to the product of their charges divided by the square of the distance between them.

## What is the significance of having a net force of zero on a charged particle?

A net force of zero on a charged particle means that the particle is in a state of equilibrium, where all the forces acting on it are balanced. This is important because it allows the particle to remain in a stable position without moving or accelerating.

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