Why is the kinetic energy of current carriers associated with their ordered
motion not taken into account when considering the electric current in a sub-
stance?
@@ -8,17 +8,15 @@Statement
Estimate the kinetic energy of one electron (in electron volts) at a
current of I = 100 A in a sodium wire with a cross-section of S = 1 mm2The
−
number of conduction electrons per unit volume of the wire ne= 2.5·1022cm−3.
+
number of conduction electrons per unit volume of the wire ne= 2.5·10^22cm^−3.
### Solution
Let's start with the first part: Why is the kinetic energy of ordered motion not considered in electric current?
When a potential difference is established, the free electrons in a conductor acquire a small net drift velocity v_d superimposed on their random thermal motion. The thermal velocity of electrons at room temperature is on the order of 10^5\ \text{m/s}, corresponding to a thermal kinetic energy on the order of kT \approx 0.025\ \text{eV}. In contrast, the drift velocity is several orders of magnitude smaller.
The kinetic energy associated with ordered motion is proportional to v_d^2, so it is extremely small compared with thermal energy and, above all, with the Fermi energy in metals (several eV). Consequently, when studying the energy balance of a circuit, the contribution of this ordered kinetic energy is absolutely negligible compared with the interaction energies and the energy dissipated by the Joule effect. For this reason, models ignore this small net kinetic energy and focus on the charge flow and collision losses.
−
−
---
Second part: Estimation of the kinetic energy of one electron
Data:
Current:$ I = 100\ \text{A}$
Cross‑section of the sodium wire:$ S = 1\ \text{mm}^2 = 1 \times 10^{-6}\ \text{m}^2$
Density of conduction electrons: $n_e = 2.5 \times 10^{22}\ \text{cm}^{-3} = 2.5 \times 10^{28}\ \text{m}^{-3}$
Why is the kinetic energy of current carriers associated with their ordered
Why is the kinetic energy of current carriers associated with their ordered
motion not taken into account when considering the electric current in a sub-
motion not taken into account when considering the electric current in a sub-
stance?
stance?
@@ -8,17 +8,15 @@Statement
Estimate the kinetic energy of one electron (in electron volts) at a
Estimate the kinetic energy of one electron (in electron volts) at a
current of I = 100 A in a sodium wire with a cross-section of S = 1 mm2The
current of I = 100 A in a sodium wire with a cross-section of S = 1 mm2The
number of conduction electrons per unit volume of the wire ne= 2.5·1022cm−3.
number of conduction electrons per unit volume of the wire ne= 2.5·10^22cm^−3.
### Solution
### Solution
Let's start with the first part: Why is the kinetic energy of ordered motion not considered in electric current?
Let's start with the first part: Why is the kinetic energy of ordered motion not considered in electric current?
When a potential difference is established, the free electrons in a conductor acquire a small net drift velocity v_d superimposed on their random thermal motion. The thermal velocity of electrons at room temperature is on the order of 10^5\ \text{m/s}, corresponding to a thermal kinetic energy on the order of kT \approx 0.025\ \text{eV}. In contrast, the drift velocity is several orders of magnitude smaller.
When a potential difference is established, the free electrons in a conductor acquire a small net drift velocity v_d superimposed on their random thermal motion. The thermal velocity of electrons at room temperature is on the order of 10^5\ \text{m/s}, corresponding to a thermal kinetic energy on the order of kT \approx 0.025\ \text{eV}. In contrast, the drift velocity is several orders of magnitude smaller.
The kinetic energy associated with ordered motion is proportional to v_d^2, so it is extremely small compared with thermal energy and, above all, with the Fermi energy in metals (several eV). Consequently, when studying the energy balance of a circuit, the contribution of this ordered kinetic energy is absolutely negligible compared with the interaction energies and the energy dissipated by the Joule effect. For this reason, models ignore this small net kinetic energy and focus on the charge flow and collision losses.
The kinetic energy associated with ordered motion is proportional to v_d^2, so it is extremely small compared with thermal energy and, above all, with the Fermi energy in metals (several eV). Consequently, when studying the energy balance of a circuit, the contribution of this ordered kinetic energy is absolutely negligible compared with the interaction energies and the energy dissipated by the Joule effect. For this reason, models ignore this small net kinetic energy and focus on the charge flow and collision losses.
---
Second part: Estimation of the kinetic energy of one electron
Second part: Estimation of the kinetic energy of one electron
Data:
Data:
Current:$ I = 100\ \text{A}$
Current:$ I = 100\ \text{A}$
Cross‑section of the sodium wire:$ S = 1\ \text{mm}^2 = 1 \times 10^{-6}\ \text{m}^2$
Cross‑section of the sodium wire:$ S = 1\ \text{mm}^2 = 1 \times 10^{-6}\ \text{m}^2$
Density of conduction electrons: $n_e = 2.5 \times 10^{22}\ \text{cm}^{-3} = 2.5 \times 10^{28}\ \text{m}^{-3}$
Density of conduction electrons: $n_e = 2.5 \times 10^{22}\ \text{cm}^{-3} = 2.5 \times 10^{28}\ \text{m}^{-3}$
