Question

A beam of electrons moving at a speed of ${10}^6$ m/s along a line produces a current of $1.6\times {10}^{-6}A$. The number of electrons in the 1 metre of the beam is

• A. ${10}^6$
• B. ${10}^7$
• C. ${10}^{13}$
• D. ${10}^{19}$

Answer 1

The correct option is B ${10}^7$

$i=\frac{q}{t}=\frac{q}{\left(\frac{x}{v}\right)}=\frac{qv}{x}=\frac{nev}{x}\Rightarrow n=\frac{ix}{ev}=\frac{1.6\times {10}^{-6}\times 1}{1.6\times {10}^{-19}\times {10}^6}={10}^7$