a system of two point charges has zero potential energy only when
That’s correct! In a system of two point charges, the potential energy will be zero when the charges have cancelled out each other. Let’s explore this concept further.
When we have two point charges in a system, the potential energy between them is given by Coulomb’s law:
U = \frac{{k \cdot q_1 \cdot q_2}}{{r}}
In this equation, U represents the potential energy, (k) is the electrostatic constant, q_1 and q_2 are the magnitudes of the charges, and (r) is the distance between the charges.
In order for the potential energy to be zero, the numerator of the equation, q_1 \cdot q_2, must be equal to zero. This means that either one or both of the charges must be zero.
If one of the charges is zero, we have a neutral system since there is no charge present to interact with the other charge. In this case, the potential energy will be zero.
Similarly, if both charges have equal magnitudes but opposite signs (q_1 = -q_2), the net charge of the system is zero and the potential energy will also be zero.
Therefore, for a system of two point charges to have zero potential energy, the charges must either cancel each other out or one of the charges must be zero.
I hope this explanation clarifies the concept for you! Let me know if you have any further questions.