Question

A straight conductor of uniform cross-section carrier a current $I$. Let $s$ be the specific charge of an electron. The momentum of all the free electrons per unit length of the conductor, due to their drift velocities only, is

• A. $I/s$
• B. $\sqrt{I/s}$
• C. $Is$
• D. $(I/s{)}^2$

Answer 1

The correct option is A $I/s$

If electron are moving with drift velocity $V_d,A$ is area of cross-section and $n$ is the number of free electrons per unit volume.

Then we know that,

$I=neA{V}_d$

And given that
$s=\frac{e}{m}(m=\text{mass of electron})$

$\Rightarrow e=ms$

$\therefore I=n\left(ms\right)A{V}_d$

$\Rightarrow I/s=nmA{V}_d.......\left(1\right)$

Now, no. of free electrons per unit length $=nA$

So, momentum $p$ of $nA$ electrons is

$p=nAm{V}_d$

From eq. $\left(1\right)$,

$p=nAm{V}_d=I/s$

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