# Electrical Force Decreased by 1/4 When Particles Moved Half as Far Apart

• weemanbran
In summary, the magnitude of electrical force between two charged particles is four times greater when the distance between them is halved. This is because the distance, which is in the denominator of Coulomb's Law, becomes squared when it is halved, resulting in a larger ratio and therefore a larger force.

## Homework Statement

The magnitude of electrical force between a pair of charged particles is _____ as much when the particles are moved half as far apart.

## The Attempt at a Solution

I understand that Coulomb's Law is.

F = k q1 q2 / d^2

So is the answer just putting in the distance which is 1/2 and squaring it? So is it just 1/2^2?

Be careful -- the distance between particles appears in the denominator of Coulomb's Law. So if the distance is halved, what happens to this ratio?

If the distance distance is halved then the ratio would increase... I just don't know by how much...

Will the force increase or decrease? and by what factor? Hint: What is $$(\frac{1}{2})^2$$?

konthelion said:
Will the force increase or decrease? and by what factor? Hint: What is $$(\frac{1}{2})^2$$?

I think you mean $$\frac{1}{(\frac{1}{2})^2}$$ ; the halved distance is in the denominator for Coulomb's Law...

## 1. What is the relationship between electrical force and distance?

The electrical force between two charged particles is inversely proportional to the square of the distance between them. This means that as the particles move farther apart, the force decreases, and as they move closer together, the force increases.

## 2. How does the electrical force change when the particles move half as far apart?

If the distance between two charged particles is halved, the electrical force will increase by a factor of four. This is because the distance is squared in the equation for electrical force, so halving the distance will result in 1/2 squared, which is 1/4. Therefore, the electrical force will be four times greater.

## 3. Why does the electrical force decrease by 1/4 when particles move half as far apart?

This is due to the inverse square law, which states that the force between two charged particles is inversely proportional to the square of the distance between them. When the distance is halved, the force increases by a factor of four, and when the distance is doubled, the force decreases by a factor of four.

## 4. Is there a limit to how far apart particles can be and still experience an electrical force?

Technically, there is no limit to how far apart particles can be and still experience an electrical force. However, as the distance between particles increases, the force becomes weaker and eventually becomes negligible. This distance is determined by the strength of the charges and the charges of the particles involved.

## 5. How does the electrical force between particles compare at different distances?

The electrical force between particles is strongest when the particles are closest together and decreases as the distance between them increases. However, it is important to note that the force never completely disappears, as it is always present between charged particles regardless of distance.

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