To translate the movement of an electron into a hypothetical current, we need to consider the properties of electric charge and how it relates to current.
Current (I) is defined as the rate of flow of electric charge (Q) through a given area per unit of time. It is expressed in units of amperes (A). In the case of electrons, the charge carried by each electron is negative (q = -e), where e is the elementary charge and has a value of approximately -1.602 x 10^-19 coulombs.
To determine the hypothetical current (I) based on the electron's movement, we need to know the number of electrons passing through a specific point per unit time. This quantity is related to the electron's speed (u) and the cross-sectional area (A) perpendicular to its motion.
The equation relating current, charge, and time is: I = ΔQ/Δt,
where ΔQ is the change in charge passing through the cross-sectional area A in the time interval Δt.
Since we are considering a single electron, ΔQ is the charge of a single electron, -e. Therefore, we can express the current as: I = -e/Δt.
Now, to relate the electron's speed (u) to the time interval Δt, we need to consider the distance traveled by the electron in that time. Let's assume the electron moves a distance d in the time Δt. The velocity (v) of the electron is given by: v = d/Δt.
The electron's speed (u) can be defined as the magnitude of the velocity: u = |v| = |d/Δt|.
From the definition of current (I) and using the relation between velocity (v) and speed (u), we can rewrite the equation as: I = -e/Δt = -e/(d/u) = -e(u/d).
In this equation, the term (u/d) represents the number of times the electron crosses the area A per unit time, which can be thought of as the electron's "frequency" of crossing the area.
Therefore, the hypothetical current (I) can be expressed as: I = -e(u/d).
Note that this is a hypothetical current and assumes the motion of a single electron. In practical situations, the current is typically the collective motion of a large number of electrons. To calculate the actual current in a conductor, we need to consider the number of charge carriers (e.g., electrons per unit volume) and their velocity distribution, which can be determined by factors such as the applied voltage, temperature, and material properties.