Question

A charged spherical particle of radius $5000\text{Å}$ moves with constant horizontal speed of $2\text{cm/s}$ in a horizontal electric field of $6.28\times {10}^6\text{V/m}$. Find the number of excess electrons in it $(\pi =3.14)$. The surrounding medium is air with coefficient of viscosity $\eta =1.6\times {10}^{–5}{\text{N-s/m}}^2$. (Neglect gravity)

Answer 1

Given that the particle moves with constant speed, so net force is zero.
$F_{viscous}=F_e$
$6\pi \eta rv=qE=neE$,
where $n$ is number of electrons
$\Rightarrow 6\times 3.14\times 1.6\times {10}^{-5}\times 5\times {10}^{-7}\times 2\times {10}^{-2}=n\times 1.6\times {10}^{-19}\times 6.28\times {10}^6$
$\Rightarrow n=3$