# How exactly do you find the net force between charges?

• paki123
In summary, the conversation discussed the electrical force between two protons, which follows the formula k*q1*q2/r^2 and acts in the opposite direction. It was also mentioned that with equal distances and opposite directions, the net force would be 0. The question of whether a third electron could be added and still maintain a net force of 0 was also posed and answered in the affirmative, with the explanation of equal and opposite forces between all particles.
paki123
I was doing some homework problems, and I came across a couple I didn't know. I then realized I must have screwed up my understanding on electrical forces.

For an electrical force, if there are two protons, the force is k*q1*q2/r^2. The direction is in the opposite direction.

<---(+) (+)--->

Right?

What would be the net force there assuming the charge is e? Would it be 0 since they are in the opposite direction and have equal distances?

My question is it possible to have a third electron and still have the net force equal to 0?

Yes and Yes! If $\textbf{F}_{i, j}$ means the force that charged particle j exerts on charged particle i, then $\textbf{F}_{i, j}$ = $\textbf{F}_{j, i}$. In other words the forces between the particles are equal and opposite.

For three particles,
the force on particle 1 is $\textbf{F}_{1, 2}$ + $\textbf{F}_{1, 3}$
the force on particle 2 is $\textbf{F}_{2, 3}$ + $\textbf{F}_{2, 1}$
the force on particle 3 is $\textbf{F}_{3, 1}$ + $\textbf{F}_{3, 2}$

So the net force, that is the forces on all three particles added together, is zero, because
$\textbf{F}_{1, 2}$ = $-\textbf{F}_{2, 1}$ and so on.

## 1. How do you calculate the net force between charges?

The net force between charges is calculated using Coulomb's Law, which 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. The formula for calculating net force between two charges is F = (k * q1 * q2) / r2, where k is the Coulomb's constant, q1 and q2 are the charges, and r is the distance between them.

## 2. What is Coulomb's constant and why is it important?

Coulomb's constant, denoted by k, is a proportionality constant that relates the force between two charges to the magnitude of the charges and the distance between them. Its value is 8.99 x 109 N*m2/C2. It is important because it allows us to quantitatively calculate the force between charges and understand the relationship between the magnitude of the charges and the distance between them.

## 3. How does the distance between charges affect the net force?

The distance between charges has an inverse square relationship with the net force. This means that as the distance between charges increases, the force between them decreases. Conversely, as the distance between charges decreases, the force between them increases. This relationship is described by the inverse square law in Coulomb's Law.

## 4. What is the direction of the net force between charges?

The direction of the net force between charges is along the line connecting the two charges. If the charges have the same sign (both positive or both negative), the force will be repulsive and will push the charges away from each other. If the charges have opposite signs (one positive and one negative), the force will be attractive and will pull the charges towards each other.

## 5. Can the net force between charges ever be zero?

Yes, the net force between charges can be zero if the charges have the same magnitude and are placed at equal distances from a third charge. This is known as the neutral point and occurs when the attractive force between the two charges is equal in magnitude but opposite in direction to the repulsive force from the third charge. In this case, the net force on each charge is zero, resulting in a state of equilibrium.

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