Three 1.0 μC charges are placed along the x-axis, one charge at x = −10 cm, another at the origin, and the last one at x = 10 cm. What is the total potential energy of this arrangement?

Question

Quizplus · Accepted Answer

The total potential energy of a system of charges is given by the sum of the potential energies due to each pair of charges. The potential energy $U$ between two point charges is given by $U = \frac{kq_1q_2}{r}$, where $k$ is Coulomb's constant ($8.99 \times 10^9 \, \text{N m}^2/\text{C}^2$), $q_1$ and $q_2$ are the charges, and $r$ is the distance between them. Here, all charges are $1.0 \, \mu C = 1.0 \times 10^{-6} \, C$, and the distances between them are $20 \, cm = 0.2 \, m$ for the charges at the ends and $10 \, cm = 0.1 \, m$ for each charge from the center to an end. Calculating the potential energy for each pair and summing gives a total potential energy of approximately $0.22 \, J$.

Three 10 μC Charges Are Placed Along the X-Axis, One Charge