# Velocity of Three Charges Released from Equilateral Triangle

• Ichigo449
In summary, three equal charges with charge q and mass m are placed into an equilateral triangle of side length L. The speed of each charge when they are infinitely far from one another is √(1/2πε [q^2 /L]).
Ichigo449

## Homework Statement

Three equal charges with charge q and mass m are placed into an equilateral triangle of side length L. Find the speed of each when they are infinitely far from one another.

## Homework Equations

-ΔU =ΔK (since the electric force is conservative), U= 1/4πε Σq1q2 /r

## The Attempt at a Solution

Since the charges are equal and in an equilateral triangle U =1/4πε (3q^2 /L). Conservation of energy gives that ΔK =U, since U at infinity is 0. By conservation of momentum each charge will move at the same velocity so 1/2mv^2 +1/2mv^2 +1/2mv^2 = 1.5mv^2 =U. Implying v = √(1/6πε [3q^2 /L]).
Any errors in the above reasoning or a better way of laying out the solution?

It is correct, but you can simplify the result.

## 1. How is the velocity of three charges released from an equilateral triangle calculated?

The velocity of three charges released from an equilateral triangle is calculated using the equation v = √(q/πε) where v is the velocity, q is the charge, and ε is the permittivity of the medium. This equation takes into account the repulsive force between the charges and the distance between them.

## 2. What is an equilateral triangle and why is it important in this scenario?

An equilateral triangle is a triangle with three equal sides and three equal angles. In this scenario, it is important because it allows for equal distribution of charges and creates a symmetrical system for calculating the velocity of the charges.

## 3. How does the distance between the charges affect the velocity?

The distance between the charges has a significant effect on the velocity. The farther apart the charges are, the smaller the velocity will be due to the decreased repulsive force between them. On the other hand, if the charges are closer together, the velocity will be larger due to the increased repulsive force.

## 4. Is the velocity of the charges released from an equilateral triangle always the same?

No, the velocity of the charges can vary depending on the charge and the distance between them. However, for an equilateral triangle with identical charges, the velocities will be the same. If the charges or the distance between them is different, then the velocities will also be different.

## 5. Can the velocity of the charges released from an equilateral triangle be measured experimentally?

Yes, the velocity of the charges can be measured experimentally using various methods such as a ballistic galvanometer or a charged particle beam. However, it is important to note that other external factors such as air resistance and electromagnetic interference can affect the measurement.

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