# Coulomb's Law (3 charges in equilateral triangle)

• BMcC
In summary: After doing some more research, I've found that the sign on the x components is actually the opposite of what it is shown in the diagram. The x components have a negative sign, meaning that the force acts away from the other charge. I've included a picture to better illustrate my point. Please help me understand why the x components have a negative sign.
BMcC
Three charged particles are placed at the corners of an equilateral triangle of side L = 1.74 m.
The charges are q1 = 3.63 µC, q2 = −8.05 µC, and q3 = −6.31 µC. Calculate the magnitude and direction (counterclockwise from the positive x axis) of the net force on q1 due to the other two charges.

First, I converted the charges from µC to C

q1 = 3.63e-6 C
q2 = -8.05e-6 C
q3 = -6.31e-6 C

Then I used Coulomb's law to figure out the forces on q1 from the other 2 charges

F21 = the force applied to charge 1 by charge 2
F31 = the force applied to charge 1 by charge 3
r = the distance between each charge = 1.74m

F21 = K*q1*q2 / r2
= (8.998e9)(3.63e-6)(-8.05e-6) / 1.742
= -0.0868 N

F31 = (8.998e9)(3.63e-6)(-6.31e-6) / 1.742
= -0.0681 N

Now because these forces applied are on the diagonal of that equilateral triangle, I must find the x and y components of the forces. The angle inside any equilateral triangle is 60 degrees, so I'm using 60 for my trig here.

x

(-0.0868 * cos60) + (-0.0681 * cos60) = -0.0774 N

y

(-0.0868 * sin60) + (-0.0681 * sin60) = -0.134 N

To find the magnitude, I've been adding the square of the x and y component, then taking the square root of it.

sqrt[(-0.0774 N)2 + (-0.134 N)2] = 0.155 N

I'm not sure if this is correct, nor am I sure how to get the direction in degrees. This method of finding the force makes sense to me but I need to submit both the magnitude and direction at the same time to get the answer correct.

The magnitude of the forces is positive, the - sign indicates that the force acts towards the other charge. Draw the individual forces. Do the x components have the same (negative) sign? ehild

Not quite sure I understand what you mean by - sign indicating that the force acts towards the other charge. Care to explain a little further?

You wrote that F21 = -0.0868 N and F31= -0.0681 N. Are those forces parallel? What does the negative sign mean?
You also considered both x components negative. With respect to what?

ehild

I was just going under what the question gave me in terms of q2 and q3's charges. They are both negative charges, therefor wouldn't the Force come out negative just in terms of signage? I suppose this is where I'm confused about the question.

BMcC said:
Bump

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BMcC said:
I was just going under what the question gave me in terms of q2 and q3's charges. They are both negative charges, therefor wouldn't the Force come out negative just in terms of signage? I suppose this is where I'm confused about the question.

All that the negative sign means is that the force is attractive.

You need to use the geometry of the problem to get the components of the Force(s) .

The forces have direction, (see picture) determine the x and y components accordingly.

ehild

#### Attachments

• threecharges.JPG
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## 1. What is Coulomb's Law?

Coulomb's Law is a fundamental law of electrostatics that describes the force between two charged particles. It states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

## 2. How does Coulomb's Law apply to three charges in an equilateral triangle?

In this scenario, Coulomb's Law can be used to calculate the net force on any of the three charges due to the other two charges. The force on each charge will depend on the magnitude and direction of the charges and the distances between them.

## 3. What is the equation for calculating the force between three charges in an equilateral triangle?

The equation for calculating the force between three charges in an equilateral triangle is F = k(q1q2/r^2), where F is the force, k is the Coulomb's constant, q1 and q2 are the charges, and r is the distance between them.

## 4. How do the positions of the charges affect the net force in an equilateral triangle?

The positions of the charges can affect the net force in an equilateral triangle in various ways. If the charges are evenly spaced in the triangle, the net force on each charge will be equal and opposite, resulting in a zero net force. However, if the charges are not evenly spaced, the net force on each charge will be different and may result in a non-zero net force on one or more charges.

## 5. What is the significance of an equilateral triangle in Coulomb's Law?

An equilateral triangle is often used in Coulomb's Law problems as it simplifies the calculations and allows for easier visualization of the forces between the charges. It is also a common geometric arrangement for three charges in real-life scenarios, such as atoms and molecules.

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