A total of $5.0 × 10^{16}$ electrons per second go through a conductor of area of cross-section $2\, mm^2$. The current density will be

$4 × 10^3\, A m^{-2}$

The correct answer is Option (2) → $4 × 10^3\, A m^{-2}$

Given:

Number of electrons per second, $n = 5.0 \times 10^{16} \ \text{s}^{-1}$

Cross-sectional area, $A = 2 \ \text{mm}^2 = 2 \times 10^{-6} \ \text{m}^2$

Charge of one electron, $e = 1.6 \times 10^{-19} \ \text{C}$

Current, $I = n \cdot e = (5.0 \times 10^{16}) \cdot (1.6 \times 10^{-19}) = 8.0 \times 10^{-3} \ \text{A}$

Current density, $J = \frac{I}{A} = \frac{8.0 \times 10^{-3}}{2 \times 10^{-6}} = 4.0 \times 10^{3} \ \text{A/m}^2$

Current density, $J = 4.0 \times 10^3 \ \text{A/m}^2$