# Equation for speed of charges (electrostatics)?

• devil0150
In summary, the problem involves finding the speed of two particles with given mass and charge when their distance becomes 0.5 m. There is no direct equation in the book that links speed and charges, but there are equations that relate charge, distance, force, mass, acceleration, and speed. Using Coulomb's law, the force between the particles can be found, but the acceleration is not constant due to the varying force at different positions. In this case, considering conservation laws may be helpful in solving the problem.
devil0150
I am trying to do an exercise but there's no equation in the book that links speed and charges. Can anyone help? This is the exercise:

## Homework Statement

There is a particle with mass = 20 grams and charge = 6 x 10^(-6) C, and another particle with mass = 50 grams and charge = -4 x 10^(-6) C. The distance between the particles is 1 m. Find the speed of each particle when their distance becomes 0.5 m.

devil0150 said:
there's no equation in the book that links speed and charges.
Not directly, but I'm sure you have equations that relate charge and distance to force, force and mass to acceleration, acceleration and distance to speed.

Yes I tried using coulomb's law to find the force, and then each of the accelerations (a = F/m) but to find the speed from this (v^2 = 2*a*d) I need the individual distance traveled by each particle, and I only have the sum of both distances (0.5 m).

Edit: And since the force has different value for different positions of the particles, doesn't that mean that the acceleration isn't constant? How can I find the speed using a non-constant acceleration?

Last edited:
devil0150 said:
Edit: And since the force has different value for different positions of the particles, doesn't that mean that the acceleration isn't constant? How can I find the speed using a non-constant acceleration?

In such cases it's often profitable to consider the problem in terms of conservation laws

The equation for the speed of charged particles in electrostatics is given by:

v = √(2qV/m)

where v is the speed of the particle, q is the charge of the particle, V is the potential difference between the particles, and m is the mass of the particle.

In this exercise, the potential difference between the particles is given by:

V = kq1q2/d

where k is the Coulomb's constant (9x10^9 Nm^2/C^2), q1 and q2 are the charges of the two particles, and d is the distance between them.

Substituting the given values, we get:

V = (9x10^9)(6x10^-6)(-4x10^-6)/(1m) = -2.16x10^-2 V

Now, using the above equation for speed and substituting the values for each particle, we get:

Particle 1: v1 = √(2(6x10^-6)(-2.16x10^-2)/(20x10^-3)) = 3.87x10^4 m/s

Particle 2: v2 = √(2(-4x10^-6)(-2.16x10^-2)/(50x10^-3)) = 1.55x10^4 m/s

Therefore, the speed of each particle when their distance becomes 0.5 m is 3.87x10^4 m/s and 1.55x10^4 m/s for Particle 1 and Particle 2, respectively.

## What is the equation for the speed of charges in electrostatics?

The equation for the speed of charges in electrostatics is v = E/q, where v is the speed of the charge, E is the electric field strength, and q is the magnitude of the charge.

## How do I calculate the speed of a charged particle using this equation?

To calculate the speed of a charged particle, you need to know the electric field strength and the magnitude of the charge. Simply plug these values into the equation v = E/q and solve for v.

## What is the unit for the speed of charges in electrostatics?

The unit for the speed of charges in electrostatics is meters per second (m/s).

## Can this equation be used for both positive and negative charges?

Yes, this equation can be used for both positive and negative charges. The sign of the charge, whether positive or negative, will affect the direction of the velocity, but the magnitude of the charge is what is used in the calculation.

## Are there any other factors that can affect the speed of charges besides the electric field strength and magnitude of the charge?

Yes, there are other factors that can affect the speed of charges, such as the presence of other charges, the medium through which the charge is traveling, and external forces acting on the charged particle.

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