Question

Three charged [particles are initially in position-1. They are free to move and they come to position-2, after some time let ${{U}_{1}}\text{ and }{{U}_{2}}$be the electrostatic potential energies in position-1 and position-2. Then
A. ${{U}_{1}}={{U}_{2}}$
B. ${{U}_{2}}\ge {{U}_{1}}$
C. ${{U}_{2}}>{{U}_{1}}$
D. ${{U}_{1}}>{{U}_{2}}$

Answer 1

Hint: understand what electrostatic potential energy is. Try to see how a charged particle behaves in a potential field. Compare with the motion of particles in nature in a potential with the free charged particle in a potential field. On the basis of this give your answer.

Complete step by step answer:
Electrostatic potential can be defined as the work done to move a unit charge to a point with reference to another point through a field without accelerating it.
Electrostatic potential energy can be defined as the energy possessed by a unit positive charge when it is at a specific point with reference to another point.
A free charge can move through space freely. In nature an object will always move from a high energy point to a low energy one. A free charge will aso always move from a higher potential point to a lower potential point.
In this question also, the three charges are free charge which are at position-1 and can move freely. The potential energy at position 1 is ${{U}_{1}}$. The charges are free to move and they will only move to a point with lower potential energy. So, if the charges move to another position with potential energy ${{U}_{2}}$, then the potential energy of the second or final position must be lower than the initial position. So, the potential ${{U}_{1}}$ is greater than the potential ${{U}_{2}}$.
The correct option is (D)
Note: we have seen that the charged particle or any other natural object will always try to reduce its potential energy and try to move to a position with lower potential energy. To move from a higher potential point to a lower potential point we do need any to do any work. That’s why a free particle can move in the [potential field without any external force.