To determine the weakest electrostatic force of repulsion among positive charges, it's essential to consider Coulomb's law, which states that the force ( F ) between two charges ( q_1 ) and ( q_2 ) separated by a distance ( r ) is given by the formula:
[
F = k \frac{{|q_1 \cdot q_2|}}{{r^2}}
]
where ( k ) is Coulomb's constant. According to this law, the force of repulsion increases as the distance between the charges decreases, since the force is inversely proportional to the square of the distance (( r^2 )).
Given this relationship, when the distance between the charges increases, the force of repulsion becomes weaker. Therefore, the largest distance provided in the options would yield the weakest repulsive force.
Charges at 4 cm apart experience the weakest electrostatic force of repulsion compared to the other sets of distances. As the distance increases from 1 cm to 4 cm, the electrostatic force decreases significantly because the force is inversely proportional to the square of the distance. This means that at 4 cm, the charges experience the greatest separation, resulting in