Question

A particle is attached to a spring and is pushed so that the spring is compressed more and more. As a result, the spring exerts a greater and greater force on the particle. Similarly, a charged particle experiences a greater and greater force when pushed closer and closer to another particle that is fixed in position and has a charge of the same polarity. In spite of the similarity, the charged particle will not exhibit simple harmonic motion on being released, as will the particle on the spring. Explain why not.

Answer 1

In order for particles to perform a simple harmonic motion, we must follow the law of force of the form F = -kx, where x is the displacement of the object from the equilibrium position and k is the spring constant. The force shown in F = -kx is always the restoring force in the sense that the particles are pulled towards the equilibrium position.

The repulsive force felt when the charge q1 is pushed into another charge q2 of the same polarity is given by Coulomb's law
                                F = k *q1* q2 / r^2.
It is clear that Coulomb's law is an inverse-square relationship. It does not have the same mathematical form as the equation F = -kx. Thus, charged particles pushed towards another fixed charged particle of the same fixed polarity do not show a simple harmonic motion when released. Coulomb's law does not describe restoring force. When q1 is released, it just fly away from q2 and never returns.