Final answer:
The electric potential energy of a dust particle is calculated as the product of its charge and the electric potential at its position. Specific information on surrounding charges and distances is required to provide an accurate value.
Step-by-step explanation:
The question pertains to finding the electric potential energy of a dust particle with a given mass and charge in a specific scenario. Since gravitational potential energy is to be disregarded, we focus solely on the electric aspect of potential energy.
The electric potential energy (U) of a charged particle in an electric field is given by the product of its charge (q) and the electric potential (V) at its position: U = qV.
To determine the particle's potential energy, we first need to know the electric potential at the particle's position, which is typically derived from the configuration of nearby charges and their respective distances from the particle.
However, without information on the electric potential (V) at the dust particle's position in the question, we cannot calculate the potential energy directly.
If details about the surrounding charges and the particle's position relative to them are provided, one could use the formula U = k * Q * q / r, where k is Coulomb's constant (8.99 × 10^9 N·m^2/C^2), Q is the charge creating the potential, q is the charge of the particle, and r is the distance between the charges.