91Ó°ÊÓ

Quarks are fundamental particles that carry a specific type of electric charge. They are smaller constituents of protons and neutrons in an atom. Each type of quark has its own unique charge value.
In the context of this exercise, we are primarily concerned with the "up" and "down" quarks. An "up" quark carries a charge of \(+\frac{2}{3}e\), where \(e\) is the elementary charge, approximately \(1.602 \times 10^{-19} \, \text{C}\).
On the other hand, a "down" quark carries a charge of \(-\frac{1}{3}e\). The quarks combine in specific ways to form neutrons and protons. In a neutron, one "up" quark and two "down" quarks balance to achieve an overall charge of zero. This is because the sum of charges \([+\frac{2}{3}e + (-\frac{1}{3}e) + (-\frac{1}{3}e)]\) equals zero.

• "Up" quark: Charge of \(+\frac{2}{3}e\)
• "Down" quark: Charge of \(-\frac{1}{3}e\)
• Neutron: Net charge of zero

The electrostatic force is the interaction between charged objects. This force can either attract or repel depending on the charges involved.
Coulomb's Law gives us a precise way to calculate this force. It states that the magnitude of the force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:\[ F = k \frac{|q_1 q_2|}{r^2} \]Where:

• \( F \) is the electrostatic force
• \( q_1 \) and \( q_2 \) are the magnitudes of the charges
• \( r \) is the distance between the charges
• \( k \) is Coulomb's constant

This force is essential for understanding interactions at a subatomic level, such as in this exercise involving quarks inside a neutron.

Coulomb's constant (\( k \)) is a key part of Coulomb's Law and determines the strength of the electrostatic force between two charges. Its value is approximately \(8.9875 \times 10^9 \, \text{N m}^2/\text{C}^2\).
This constant quantifies how the force between two point charges behaves as a function of distance in the medium of vacuum.

• Historical Background: Named after the French physicist Charles-Augustin de Coulomb, who first described this force, it is a standard value used in electrostatic calculations.
• Physical Meaning: Coulomb's constant shows the force in Newtons between two charges of one Coulomb each, when they are separated by a meter of distance.
• Uses: It helps predict forces in atomic and molecular scales, which is critical for understanding how particles such as quarks behave in nuclear particles.