Final answer:
The current density in a copper wire with a cross-sectional area of 10⁻⁷ m² carrying a 1.5 A current is 1.5 × 10⁷ A/m². To find the average drift velocity of conduction electrons, we use the known values of current, free electron density, electron charge, and cross-sectional area.
Step-by-step explanation:
Current Density and Average Drift Velocity Calculation
To calculate the current density (J) in a copper wire with a cross-sectional area (A) of 10⁻⁷ m² carrying a current (I) of 1.5 A, we use the formula:
J = I/A
Substituting the given values:
J = 1.5 A / 10⁻⁷ m² = 1.5 × 10⁷ A/m²
The current density is 1.5 × 10⁷ A/m².
To calculate the average drift velocity (vd), we use the formula:
I = nqAvd
where:
- n is the free electron density (8 × 10²⁸ electrons/m³)
- q is the charge of an electron (1.60 × 10⁻¹¹ C)
- A is the cross-sectional area (10⁻⁷ m²)
Rearranging the formula to solve for vd gives:
vd = I / (nqA)
Substituting the values:
vd = 1.5 A / (8 × 10²⁸ electrons/m³ × 1.60 × 10⁻¹¹ C/electron × 10⁻⁷ m²)
The average drift velocity of conduction electrons in the copper wire is calculated from the provided values.