Two identical conducting spheres, \(A\) and \(B\) carry charges \(+Q\) and \(-Q\), respectively. A third, identical conducting sphere \(C\) carries charge \(Q=0\). Sphere \(A\) is touched to sphere \(C\) and separated. Next, sphere \(B\) is touched to sphere \(C\) and separated. Finally, \(A\) is touched to \(B\) and separated. What is the final charge on each sphere? (A) \(A=Q ; B=-Q ; C=0\) (B) \(A=Q / 2 ; B=Q / 2 ; C=Q / 4\) (C) \(A=Q / 8 ; B=Q / 8 ; C=-Q / 4\) (D) \(A=Q / 2 ; B=-Q / 4 ; C=-Q / 4\) (E) \(A=Q / 4 ; B=-Q / 8 ; C=-Q / 4\)

Electric charge, often denoted by the symbol 'Q', is a fundamental property of matter that comes in two types known as positive and negative. This property is the basis for the electromagnetic interaction, which is one of the four fundamental forces in physics. Charge is quantized and occurs in discrete amounts; the elementary charge, carried by electrons and protons, is approximately equal to \(1.6 \times 10^{-19}\) coulombs.

In the context of the given problem, we look at conducting spheres, which are capable of transferring charge to one another on contact. The redistribution of charge is a result of the conductive material attempting to reach an equilibrium, where the potential difference between the touching objects is minimized. A key characteristic of conductors is that they allow charge to move freely across their surfaces. This is why when two charged conductive spheres come into contact, the charges redistribute until each sphere reaches an equal amount of charge per unit area, given that they are identical in size.

Conductivity in physics is defined as the ability of a material to allow the flow of electric charge. This is most commonly seen in metals, whose structure allows for free electrons—also known as charge carriers—to move within the material. Good conductors, like copper or silver, have a high density of these carriers, enabling efficient charge transport.

When considering our problem, the conductivity of the spheres allows for the charge to be transferred and distributed uniformly across the spheres' surface upon contact. The nature of conductive materials is essential in understanding how Sphere A, initially charged with \(+Q\), transfers half of its charge to Sphere C when they touch, due to their conductive properties. Similarly, Sphere B's interaction with Sphere C involves the flow of charge to reach a new equilibrium.

Charge conservation is a principle stating that the total electric charge in an isolated system remains constant over time. This fundamental conservation law means that the amount of charge is the same before and after any process, such as the transfer or redistribution of charge between objects. It is important to note that while charges can move and redistribute among conductive objects, the system's total charge will not change unless there is an external influence.

In our problem, this principle is at play when the spheres touch and redistribute their charges. At each step, the total system charge of Sphere A, B, and C remains constant because no external charge is added or removed. Understanding charge conservation is key to correctly determining that, after all interactions, the final charges on spheres A, B, and C must still sum to the original total, which is zero.