Solution

The electric current is defined by:

$i = \frac{dq}{dt}$

but $dq = e dn$, where e is the fundamental electrical charge and $dt = ds/c$, where c is the speed of light.

$i = ce \frac{dn}{ds}$

we can approximate $\frac{dn}{ds}$ to $\frac{n}{\ell}$, son

$i \simeq \frac{cen}{\ell} = 0.02\;\rm{A}$

b) Again, electric current can be expressed as

$i = \frac{dq}{dt} \simeq \frac{e}{t}$ (1)

Applying Newton Second Law:

$\frac{e^2}{4\pi\varepsilon r^2} = \frac{m_e v^2}{r}$

where $v = \frac{2\pi r}{t}$,

$t = \sqrt{\frac{16 (\pi r)^3 m_e}{e^2}}$ (2)

Putting (2) into (1),

$i = \sqrt{\frac{e^4}{16m_e(\pi r)^3}} = 0.0012\;\rm{A}$