Question

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

• A. $I.S$
• B. $\frac{I}{S}$
• C. $\sqrt{\frac{I}{S}}$
• D. $(\frac{I}{S}{)}^2$

Answer 1

Answer: (B)

$\frac{I}{S}$

Specific charge is charge per unit mass, $S=\frac{e}{m_e}$

Momentum of electrons per unit length $=\frac{m_{e}v}{l}$

$=\frac{\left(e/S\right)v}{l}$

$=\frac{\left(e/S\right)\left(l/t\right)}{l}$

$=\frac{e/S}{t}$

$=\frac{e/t}{S}$

$=\frac{I}{S}$