In the quark model of fundamental particles, a proton is...

In the quark model of fundamental particles, a proton is composed of three quarks: two "up" quarks, each having charge $+2 e / 3,$ and one "down" quark, having charge $-e / 3 .$ Suppose that the three quarks are equidistant from one another. Take that separation distance to be $1.32 \times 10^{-15} \mathrm{m}$ and calculate the electric potential energy of the system of (a) only the two up quarks and (b) all three quarks.

In the quark model of fundamental particles, a proton is
composed of three quarks: two "up" quarks, each having charge
$+2 e / 3,$ and one "down" quark, having charge $-e / 3 .$ Suppose that
the three quarks are equidistant from one another. Take that separation distance to be $1.32 \times 10^{-15} \mathrm{m}$ and calculate the electric
potential energy of the system of (a) only the two up quarks and
(b) all three quarks.

Key Concepts

Quark Model

The quark model is a framework in particle physics that explains hadrons (such as protons and neutrons) as composite particles made up of more elementary constituents called quarks. In this model, quarks come in different types (flavors) and possess fractional electric charges, meaning their specific combinations determine the overall charge and properties of the composite particle.

Coulomb's Law

Coulomb's Law quantifies the electric force and potential energy between two charged particles. It states that the potential energy between two point charges is proportional to the product of their charges and inversely proportional to the distance between them. This fundamental principle is used to calculate the interactions in systems of charged particles.

Electric Potential Energy

Electric potential energy is the energy stored in a system of charged particles due to their positions in an electric field. In the context of multiple charges, the total potential energy is computed by considering the energy contributions from each pair of charges, which reflects the work done against the electric forces when assembling the system.

Pairwise Interactions

When calculating the total electric potential energy for a system of several charges, the interactions are considered pairwise. This means that the energy contributions from each unique pair of charges are summed together. This approach is especially important in systems like the proton model, where the energy from different charge pairs (such as between two up quarks and between an up and a down quark) must be combined to obtain the total potential energy.

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