Which statement best describes the relationship between electric potential energy and distance in a field?

The relationship between electric potential energy and distance in an electric field is accurately represented as inversely proportional in certain contexts, particularly regarding a point charge. Specifically, as the distance from a point charge increases, the potential energy associated with the charge diminishes due to the nature of the electric field. This is defined by the equation for electric potential energy ((U)) between two point charges, which is given by

[ U = k \frac{q_1 q_2}{r} ]

where (U) is the electric potential energy, (k) is the Coulomb's constant, (q_1) and (q_2) are the magnitudes of the charges, and (r) is the distance between the charges.

As the distance ((r)) increases, the value of the potential energy ((U)) decreases, which indicates an inverse relationship. This concept is that the closer the charges are, the higher the energy due to the stronger force acting between them, and as they are separated further apart, this energy diminishes.

In certain other contexts, such as uniform electric fields (e.g., near a charged plate), electric potential energy may not strictly follow an inverse