CBSE Class 12-science Answered

The electrostatic potential energy is the energy of an electrically charged particle (at rest) in an electric field. It is defined as the work that must be done to move it from an infinite distance away to its present location, in the absence of any non-electrical forces on the object. This energy is non-zero if there is another electrically charged object nearby.

The simplest example is the case of two point-like objects A₁ and A₂ with electrical chargesq₁ and q₂. The work W required to move A₁ from an infinite distance to a distance r away from A₂ is given by:

where ?₀ is the electric constant.

This equation is obtained by integrating the coulomb force between the limits of infinity and r.

A related quantity called electric potential (commonly denoted with a V for voltage) is equal to the electric potential energy per unit charge. So as we move further potential energy will decrease.

The electron is held in a circular orbit by electrostatic attraction. The centripental force is equal to the coulomb force.

where m_e is the mass, e is the charge of the electron and k_e is coulomb's constant. This determines the speed at any radius:

It also determines the total energy at any radius:

The total energy is negative and inversely proportional to r. This means that it takes energy to pull the orbiting electron away from the proton. For infinite values of r, the energy is zero, corresponding to a motionless electron infinitely far from the proton.

Therefore, as we move away from the nucleus,kinetic energy decreases.