Question

A charged dust particle of radius $5\times {10}^{-7}m$ is located in a horizontal electric field of intensity $6.28\times {10}^{5}V/m$. The surrounding medium is air with coefficient of viscosity $1.6\times {10}^{-5}Ns/m^2$. The particle moves with a uniform horizontal speed of $0.02m/s$, then the number of excess electrons on the particle must be $10n$. Here $n=$

Answer 1

The dust particle can move with a constant speed $\left(V_T\right)$ only when the force due to $E-$ field is balanced by force of viscosity (Stoke's law)
$qE=6\pi \eta r{V}_T(\because q=Ne)$
$N\times 1.6\times {10}^{-19}\times 6.28\times {10}^5=6\times 3.14\times 1.6\times {10}^{-5}\times 5\times {10}^{-7}\times 2\times {10}^{-2}\Rightarrow N=30\Rightarrow N=10\left(3\right)\Rightarrow n=3$