91Ó°ÊÓ

Coulomb's Law is fundamental to understanding the behavior of electric charges at rest. It describes the force between two point charges as directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The equation can be expressed as

\[ F = k \frac{|q_1 \cdot q_2|}{r^2} \]
where \(F\) is the force between the charges, \(k\) is the Coulomb's constant (9.898 \times 10^9 \frac{Nm^2}{C^2}), \(q_1\) and \(q_2\) are the amount of the charges, and \(r\) is the distance between the centers of the two charges.
This principle helps explain the interaction in our example where the two metal spheres A and B influence each other through their charges, with sphere A acquiring negative charges while sphere B remains neutral. The force they exert on each other would depend on the amount of charge transferred and the distance between them, prior to the removal of the connecting plastic rod.

The electron charge, often denoted as \(e\), is a fundamental property of an electron, and it carries a constant charge of approximately \(-1.6 \times 10^{-19} \) Coulombs. This value is the basic unit of electric charge in the SI system of units, and it's essential for calculating the total charge when a certain amount of electrons are transferred or removed from an object, as illustrated in our problem.

Since the atom's neutrality is disrupted by adding or removing electrons, it acquires either a positive or negative charge. In our example, sphere A's total charge, after adding \(1.0 \times 10^{12}\) electrons, results in the total negative charge of \(-1.6 \times 10^{-7} C\), derived from the formula of charge \(Q = n \cdot e\), where \(n\) is the number of electrons. It's crucial to recognize each electron has an identical charge, which is why we can use this equation to compute the charge on sphere A.

In the exercise, knowing the difference between conductors and insulators helps us to understand the outcome. Conductors are materials that allow electrons to flow freely, thanks to the mobility of their valence electrons. Examples include metals like copper and aluminum. Insulators, on the other hand, do not easily allow the movement of electrons within them because their electrons are tightly bound to their atoms. Plastic, glass, and rubber are common insulators.

In the context of the scenario provided, when electrons are added to sphere A, it becomes negatively charged, while sphere B remains neutral as no electrons were added or removed. The connecting rod, made of insulating material (plastic), prevents any charge transfer between the spheres. So when the rod is removed, the charge on sphere A does not change, while sphere B remains neutral. This distinction is fundamental when analyzing static electricity problems and how charges distribute themselves among objects.