point charge systems.

A point charge $q_2=-0\mathrm{.}500C$ is fixed at the origin of a

coordinate system. Another point charge $q_1=1\mathrm{.}50C$ is

initially located at point $P,$ a distance $d_1=5\mathrm{.}00cm$ from

the origin along the $x$ axis. Point $R$ is located on the $x$ axis

a distance $d_2=2\mathrm{.}00cm$ from the origin, as shown

The two charges $q_3$ and $q_4$ each have a magnitude of

$-0\mathrm{.}250C,$ half of that of $q_2.$ The charges are located a

distance $a=1\mathrm{.}20cm$ from the origin along the $y$ axis,

as shown.

What is the potential energy $U_f^{\text{'}}$ of the system composed of

the three charges $q_1,q_3,$ and $q_4,$ when $q_1$ is at point $R?$

Define the potential energy to be zero at infinity.

$U_f^{\text{'}}=$