# Three Charges in a Triangle problem

• Panda_Doll
In summary, the three balls are tied to a thread and hung from a single point. The balls have the same charge, and the forces acting on the charge are equal in magnitude but not in direction.
Panda_Doll

## Homework Statement

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Three 3.0 g balls are tied to 80-cm-long threads and hung from a single fixed point. Each of the balls is given the same charge q. At equilibrium, the three balls form an equilateral triangle in a horizontal plane with 20 cm sides.

## Homework Equations

F=kq1q2/r^2

F (of 1 on 2) = F (of 2 on 1)

## The Attempt at a Solution

Since they all have the same charge, I figured that the forces would be equal at each point. All points are in the same plane, so I assumed they only have x and y components. I tried using F=kq1q2/r^2=kq2q3/r^2=kq1q3/r^2 but it ended up a huge mess with all the charges canceling. But they all have the same charge? So should I use F=k2q/r^2 and do something with that?

The forces are equal in magnitude, but not in direction.
Due to the symmetry, it is sufficient to consider the position of a single charge. What are all forces acting on it, including their directions?

What is "k2q"?

Well on each charge, since they are positioned in an equilateral triangle, they all have 2 forces acting on them, both at 30 degrees (I think?) and one would be at +30 degrees and one would be at -30 degrees.

It was supposed to be kq^2, from the F=(k*q1*q2)/r^2 equation, but since q1=q2 we could just use q^2.

Panda_Doll said:
and one would be at +30 degrees and one would be at -30 degrees.
Okay.
Panda_Doll said:
It was supposed to be kq^2, from the F=(k*q1*q2)/r^2 equation, but since q1=q2 we could just use q^2.
Right, but that is just the magnitude of the charge.

Sure, so I have the magnitude. And each charge is sitting in a triangle with sides 20cm. So, if we put the first point at say, what I'll make my origin, then I have another point 20 cm to the right, so now its coordinates are (20,0) and the third charge would be at about... (10, 17.3)? Okay. So how do their relative positions help?

mfb said:
What are all forces acting on it, including their directions?
You listed the two from the electrostatic repulsion, but there are two more. Those objects are not floating in free space.

OH! Gravity and the tension in the strings!

Right. And if you add all together, ...

## 1. What is the Three Charges in a Triangle problem?

The Three Charges in a Triangle problem is a physics problem that involves three point charges placed at the vertices of an equilateral triangle. The problem requires calculating the net electrostatic force on one of the charges due to the other two charges.

## 2. How do you solve the Three Charges in a Triangle problem?

To solve the Three Charges in a Triangle problem, you need to use the principles of Coulomb's Law, which states that the electrostatic force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. You also need to use vector addition to find the net force on the charge of interest.

## 3. What information is needed to solve the Three Charges in a Triangle problem?

To solve the Three Charges in a Triangle problem, you need to know the magnitude and sign of each charge, the distance between each pair of charges, and the angles between the lines connecting the charges. This information can be given in the problem or can be measured or calculated.

## 4. What are the units of the net electrostatic force in the Three Charges in a Triangle problem?

The units of the net electrostatic force in the Three Charges in a Triangle problem are Newtons (N), which is the unit of force in the International System of Units (SI). This is because force is a vector quantity and is measured in terms of its magnitude and direction.

## 5. How does the position of the charges affect the net electrostatic force in the Three Charges in a Triangle problem?

The position of the charges can greatly affect the net electrostatic force in the Three Charges in a Triangle problem. If the charges are placed closer together, the net force will be stronger, while placing them farther apart will result in a weaker net force. Additionally, the angles between the lines connecting the charges can also affect the magnitude and direction of the net force.

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