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Coulomb's Law is at the heart of understanding how charged particles interact. Named after Charles-Augustin de Coulomb, this fundamental principle in electromagnetism calculates the force between two point charges. The formula used is: \[ F = \frac{k \cdot |Q_1| \cdot |Q_2|}{r^2} \] where:

• \( F \) is the electrostatic force between the charges.
• \( k \) is Coulomb's constant, approximately \( 8.99 \times 10^9 \text{ N m}^2/\text{C}^2 \).
• \( Q_1 \) and \( Q_2 \) are the magnitudes of the charges.
• \( r \) is the distance between the centers of the two charges.

Coulomb's Law demonstrates that the force is inversely proportional to the square of the distance between the charges. This means that as you increase the distance between two charged objects, the force decreases rapidly. For our exercise, you calculate the tension in the string between the two boxes of protons by applying Coulomb's Law. Since the protons are identical in each box, \( Q_1 = Q_2 \). The charge of a single proton is about \( 1.6 \times 10^{-19} \text{ C} \), so for 1.0 g of protons, the total charge is significantly larger.

Gravitational force is one of the fundamental forces of nature. It describes the attraction between two masses. Isaac Newton described this force with his universal law of gravitation. The formula to compute gravitational force between two masses is: \[ F_g = \frac{G m_1 m_2}{r^2} \] Where:

• \( F_g \) is the gravitational force.
• \( G \) is the gravitational constant, approximately \( 6.674 \times 10^{-11} \text{ N m}^2/\text{kg}^2 \).
• \( m_1 \) and \( m_2 \) are the masses of the objects.
• \( r \) is the distance between the centers of the masses.

In the context of our exercise, the question asks whether the gravitational forces need to be considered. By calculating the gravitational force between the two boxes of protons, we find that due to their small mass (1.0 g each) and large separation (the distance between Earth and Moon), the gravitational force is negligible. This is in stark contrast to the much larger electrostatic force calculated using Coulomb's law.

A proton is a subatomic particle found in the nucleus of every atom. It carries a positive electrical charge of about \( 1.6 \times 10^{-19} \text{ C} \). This charge is considered the fundamental unit of positive charge, and is equal in magnitude but opposite in sign to the charge of an electron. The concept of proton charge is crucial in electromagnetism and chemistry, as it defines how protons interact with electrons and other protons.In the given exercise, understanding the proton charge helps determine the total charge of each box. Since each box contains 1.0 g of protons, we first calculate the number of protons by considering the mass of a single proton, approximately \( 1.67 \times 10^{-24} \text{ g} \). Once the number of protons \( n \) is known, the total charge \( Q \) of each box is given by \( Q = n \times 1.6 \times 10^{-19} \text{ C} \). This allows us to apply Coulomb’s Law to find the electrostatic force and, consequently, the tension in the string between the two boxes.