Question

A straight conductor of uniform cross section carries a current i. Let S be the specific charge on an electron. The momentum of all the free electrons per unit length of the conductor due to their drift velocity only is

• A. $\frac{i}{S}$
• B. $iS$
• C. ${\left(\frac{i}{S}\right)}^2$
• D. $\sqrt{\frac{i}{S}}$

Answer 1

Answer: (A)

$\frac{i}{S}$

In mechanics momentum is

$p=mv$

similarly here for electrons in conductor momentum $p_c$(say) is

$p_c=mN{v}_d$ ..........................(1)

where, m is mass of electrons, N is number of free electrons per unit length

of conductor and $v_d$ is the drift velocity.

Number of free electrons per unit length of conductor is

$N=\frac{nAl}{l}=nA$

and

$v_d=\frac{i}{neA}$

where, variables have their usual meanings.

Using above values, equation (1) becomes

$p_c=m\left(\frac{i}{neA}\right)\left(nA\right)$

$p_c=\frac{i}{\frac{e}{m}}$

$p_c=\frac{i}{S}$

where, $S=\frac{e}{m}$, specific charge on an electron.