91Ó°ÊÓ

Figure 24-26 showing four pairs of charged particles with identical separation is given.

The electric potential energy of a system of charged particles is equal to the work needed to assemble the system with the particles initially at rest and infinitely distant from each other. Thus, the potential energy of a system depends on the distance value inversely and the product of charges directly.

Formula:

The electric potential energy of the system of particles$\mathbf{U}\mathbf{=}{\mathbf{kq}}_{\mathbf{1}}{\mathbf{q}}_{\mathbf{2}\mathbf{/}\mathbf{r}}$, (i)

Let the identical separation between them be.

Now, using equation (i) for all the four arrangements, the potential energies of the arrangements can be calculated as:

Hence, the required rank of energy is $U_4=U_4>U_1=U_2$.

From equation (i), it can be clearly seen that the separation increase between the particles result in the decreasing of the potential energy of the system of charges.

Hence, the potential energy decreases.