A current of 2 A flows through a wire of cross-sectional area 25.0 mm$$^2$$. The number of free electrons in a cubic meter are $$2.0 \times 10^{28}$$. The drift velocity of the electrons is ______ $$\times 10^{-6}$$ ms$$^{-1}$$
(given, charge on electron = $$1.6 \times 10^{-19}$$ C).

We need to find the drift velocity of electrons in a wire.

Formula for drift velocity: $$I = nAv_d e$$

where $$I$$ = current, $$n$$ = number density of free electrons, $$A$$ = cross-sectional area, $$v_d$$ = drift velocity, $$e$$ = charge on electron.

Solve for $$v_d$$: $$v_d = \frac{I}{nAe}$$

Convert units and substitute: $$I = 2$$ A, $$n = 2.0 \times 10^{28}$$ m$$^{-3}$$, $$A = 25.0$$ mm$$^2 = 25.0 \times 10^{-6}$$ m$$^2$$, $$e = 1.6 \times 10^{-19}$$ C

$$v_d = \frac{2}{2.0 \times 10^{28} \times 25.0 \times 10^{-6} \times 1.6 \times 10^{-19}}$$

$$= \frac{2}{2.0 \times 25.0 \times 1.6 \times 10^{28-6-19}}$$

$$= \frac{2}{80 \times 10^{3}} = \frac{2}{8 \times 10^{4}} = 0.25 \times 10^{-4} = 25 \times 10^{-6} \text{ m s}^{-1}$$

The correct answer is 25 $$\times 10^{-6}$$ m s$$^{-1}$$.