Charge Redistribution on Conductors: Exploring the Validity of Quantization

In the discussion of electrical charge distribution among conductors, a common scenario involves applying charges to two identical conductors and then analyzing the behavior when these conductors touch and separate. Specifically, the question of what happens when two identical conductors are given charges of 1e and 2e and then brought into contact presents a fascinating case study in the principles of charge quantization. This article explores the underlying physics and provides a solution that aligns with fundamental principles of electrical engineering and quantum mechanics.

Initial Charges

We begin by establishing the initial conditions. Let us denote the charge on the first conductor as q1 and the charge on the second conductor as q2.
q1 1e
q2 2e

Total Charge Before Touching

The total charge before the conductors touch can be calculated as follows:
Qtotal q1 q2 1e 2e 3e

Touching and Redistribution of Charge

When the two identical conductors touch, charge redistributes equally between them due to the symmetry and similar capacitance of the conductors. This means that the total charge remains constant, but it is divided equally among the conductors.

The charge on each conductor after touching can be calculated as follows:
q Qtotal / 2 3e / 2 1.5e

Quantization of Charge

However, it is important to note that the phenomenon of charge quantization plays a crucial role in this context. According to quantum mechanics, charge can only take on values that are integer multiples of the elementary charge e. A charge of 1.5e violates this principle, as it is not a permissible charge in the context of charge quantization.

Given that the actual charges must be quantized, the redistribution of charge must lead to the nearest permissible values. In this scenario, the charges on the conductors must be integer multiples of the elementary charge. Therefore, when the conductors touch and then separate, they will each end up with a charge of 1e, which is the nearest quantized value.

Conclusion

In summary, when two identical conductors, initially charged to 1e and 2e respectively, are brought into contact, the charges will redistribute equally, resulting in what would be 1.5e on each conductor. However, since 1.5e is not a quantized charge, the actual distribution will occur in a way that respects the quantization of charge. Thus, both conductors will end up with a charge of 1e each after the touching and separation process.

It is important to note that this solution aligns with the principles of both electrical engineering and quantum mechanics, providing a balanced and scientifically accurate explanation of the behavior of charged conductors in this scenario.