How much work is needed to assemble an atomic nucleus...

How much work is needed to assemble an atomic nucleus containing three protons (such as Li)
if we model it as an equilateral triangle of side $2.00 \times 10^{-15}$ m with a proton at each vertex? Assume the protons started from very far away.

Key Concepts

Geometric Arrangement of Charges

The spatial configuration of charges influences the distances between them and consequently the electric potential energy of the system. In symmetric arrangements, such as an equilateral triangle, the uniform distances simplify the calculation of the pairwise potential energies and illustrate how geometric factors play a role in determining the total work or energy required for assembly.

Work in Assembling a System of Charges

The work done to assemble a configuration of point charges is equivalent to the total electric potential energy stored in the configuration. It involves calculating the energy required to bring each charge from infinity to its final position in the presence of the electric fields created by the already placed charges.

Coulomb's Law

Coulomb's Law quantifies the electrostatic force between two point charges and forms the basis for determining the potential energy between them. The law states that the force (and thus the potential energy) is directly proportional to the product of the charges and inversely proportional to the square (or first power in potential energy) of the distance between them.

Electric Potential Energy

This concept explains the energy stored due to the positions of charged particles in an electric field. When charges are brought together from infinity, work must be done against the electrostatic forces, and the energy stored in the system is calculated using the potential energy formula for point charges.

Superposition Principle

In systems with multiple charges, the total potential energy is the sum of the potential energies for each unique pair of charges. This principle allows us to calculate the overall energy by breaking down the interactions into pairwise contributions, ensuring that all interactions are accounted for correctly without double counting.

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