Question

Determine the electrostatic potential energy of a system consisting of two charges $7\text{ }\mu C$ and $-2\text{ }\mu C$ (and with no external field) placed at (−9 cm,0) and (9 cm,0) respectively.

Answer 1

In this question we have been asked to calculate the electrostatic potential energy of the system that has two charges of $7\text{ }\mu C$ and $-2\text{ }\mu C$ respectively. Therefore, to solve this question we shall use the equation for electrostatic potential energy. We know that electric potential energy is the amount of energy required to move a charge against an electric field.

Formula used:
$U=\dfrac{1}{4\pi {{\varepsilon }_{0}}}\times \dfrac{{{q}_{1}}{{q}_{2}}}{r}$
Where,
U is the electric potential energy
${{q}_{1}},{{q}_{2}}$ is the charge of the particle
r is the distance between the two particles.

Complete Step by step solution:
It is given that two charged particles are placed at (−9 cm,0) and (9 cm,0) respectively as shown in the figure below.

It is given that,
${{q}_{1}}=7\mu C$
Also,
${{q}_{2}}=-2\mu C$
Now, from the diagram we can say that,
$d=18cm$
Now, from the equation of electric potential energy
We know that,
$U=\dfrac{1}{4\pi {{\varepsilon }_{0}}}\times \dfrac{{{q}_{1}}{{q}_{2}}}{r}$
After substituting the values
We get,
$U=9\times {{10}^{9}}\times \dfrac{7\times {{10}^{-6}}\times (-2)\times {{10}^{-6}}}{0.18}$
Therefore,
$U=-0.7J$

Therefore, the electrostatic potential energy of the given system is -0.7 Joules.

Note:
Electric potential should not be confused with electric potential energy. The electric potential is the voltage applied across the system. The electric potential energy is the energy due to conservative Coulomb forces. Electric potential is the work done to bring a unit positive charge from infinity to a particular point P in the field. However, the electrostatic potential energy is the work done to bring any amount of charge from one point to the other in the electric field.