Final answer:
The potential energy of a system of eight particles with charges +3 µC placed at the corners of a cube is calculated using Coulomb's law, considering the contributions of energies along the cube's edges, face diagonals, and space diagonals, then summing these to find the total potential energy.
Step-by-step explanation:
The potential energy (U) of a system of charges is determined by the electrostatic force between each pair of charges. For our case with eight particles each with charge +3 µC placed at the corners of a cube of side 2 cm, we can use Coulomb's law to calculate the electrostatic potential energy. The energy between any two charges (q1 and q2) is given by Coulomb's law as U = k * q1 * q2 / r, where k is Coulomb's constant (8.9875 × 109 N m2/C2), and r is the distance between the charges.
Since the cube has 12 edges and each edge will be shared by two charges, we first calculate the energy for one edge and then multiply by 12 to get the total energy due to interactions along the edges. Each face diagonal will be shared by two charges as well, and the cube has 6 face diagonals, so we calculate the energy for one face diagonal and multiply by 6. For the cube's space diagonal, which is the longest diagonal inside the cube passing through its volume from one corner to the opposite corner, we calculate the energy for this once since the cube has only 4 space diagonals and each is shared by two charges.
To find the total potential energy of the system, we sum the energies for all the edges, face diagonals, and space diagonals. Throughout these calculations, we use the fact that for a cube of side L, the length of an edge is L, a face diagonal has a length of √2L, and a space diagonal has a length of √3L.