Question

A straight wire of linear change density $\lambda =2\mu \text{C/mm}$ and cross-sectional area $A=2{\text{mm}}^2$ is pulled horizontally with a constant speed of $2\text{m/s}$. The current associated due to motion of the wire will be

• A. $2\text{mA}$
• B. $4\text{mA}$
• C. $2.5\text{mA}$
• D. $5\text{mA}$

Answer 1

The correct option is B $4\text{mA}$

Given:
$\lambda =\frac{2\times {10}^{-6}\text{C}}{{10}^{-3}\text{m}}=2\times {10}^{-3}\text{C/m}$


Let the charge $dq$ crosses through a given cross-section in time $dt$

$\therefore i=\frac{dq}{dt}.......\left(1\right)$

Now, $dq=\lambda \times dl......\left(2\right)$

From $\left(1\right)\&\left(2\right)$,

$i=\frac{\lambda dl}{dt}=\lambda \left(\frac{dl}{dt}\right)$

The rate of change of length is the linear speed of wire.

Thus, $\frac{dl}{dt}=v=2\text{m/s}$

$\Rightarrow i=\lambda \times 2=\left(2\times {10}^{-3}\right)\times 2=4\times {10}^{-3}\text{A}$

$\therefore i=4\text{mA}$

Hence, option $\left(b\right)$ is correct.