Question

The potential difference across a conducting wire of length 20 cm is 30 V. If the electron mobility is $2 \times 10^{-6}$ m$^2$V$^{-1}$s$^{-1}$, then the drift velocity of the electrons is

• A. $3 \times 10^{-3}$ m/s
• B. $1.5 \times 10^{-3}$ m/s
• C. $1.5 \times 10^{-4}$ m/s
• D. $3 \times 10^{-4}$ m/s

Hint:

Mobility: $\mu = \frac{v_d}{E}$. Electric field: $E = \frac{V}{L}$.

Answer 1

The Correct Option is D

Electron mobility $\mu = \frac{v_d}{E}$, where $v_d$ is the drift velocity and $E$ is the electric field. Electric field $E = \frac{V}{L}$, where $V$ is the potential difference and $L$ is the length of the wire. $L = 20$ cm $= 0.2$ m $V = 30$ V $\mu = 2 \times 10^{-6}$ m$^2$V$^{-1}$s$^{-1}$ $E = \frac{30}{0.2} = 150$ V/m. $v_d = \mu E = (2 \times 10^{-6})(150) = 3 \times 10^{-4}$ m/s.