# Coulomb's Law and Simple Harmonic Motion

• gators1223
In summary, the problem involves two positive charges fixed on the x-axis and a third charge constrained to move only along the x-axis. By using Coulomb's Law, the force on the third charge can be calculated to be F= -4kQqs/d^3. To relate this to simple harmonic motion, the force can be compared to the force exerted by a spring in a mass, where the spring force is directly related to the displacement of the mass from equilibrium position. This can help derive an equation for the period of oscillation, T.
gators1223

## Homework Statement

Two positive charges +Q are affixed rigidly to the x-axis one at x = -d and the other at x = +d. A third charge +q of mass mwhich is constrained to move only in the x-axis is displaced from th eorigin by a small distance s << d and then released from rest. Show that q+ will execute simple harmonic motion and determine the oscillation period T.

## Homework Equations

Coulomb's Law F=kQ1Q2/r2
*possibly something else to relate this to SHM*

## The Attempt at a Solution

I found the force from coulomb's law, F= -4kQqs/d3
but i really don't know how to relate this to SHM so i can derive an equation for period.

Compare your expression for the force with the force exerted by a spring in a mass. How is the spring force related to the displacement of the mass from the equilibrium position?

## 1. What is Coulomb's Law?

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

## 2. How is Coulomb's Law expressed mathematically?

Coulomb's Law can be expressed mathematically as F = k(q1q2)/r^2, where F is the force between the two charges, k is the Coulomb constant (8.99 x 10^9 N*m^2/C^2), q1 and q2 are the charges of the particles, and r is the distance between them.

## 3. What is Simple Harmonic Motion?

Simple Harmonic Motion is a type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium and acts in the opposite direction of the displacement. This results in a sinusoidal motion.

## 4. What is the equation for Simple Harmonic Motion?

The equation for Simple Harmonic Motion is x = A sin(ωt + φ), where x is the displacement from equilibrium, A is the amplitude, ω is the angular frequency, and φ is the phase angle.

## 5. What is the relationship between Coulomb's Law and Simple Harmonic Motion?

Coulomb's Law can be applied to systems of charged particles in Simple Harmonic Motion, as the force between the particles follows the same inverse square relationship as the restoring force in Simple Harmonic Motion. This can be seen in the equation F = -kx, where x is the displacement and k is a constant related to the charges and distance between the particles.

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