Question

A charged dust particle of radius $5 \times 10^{-7} m$ is moving in a horizontal electric field of intensity $6.28 \times 10^{5} V / M$. The surrounding medium is air with coefficient of viscosity $\eta=1.6 \times 10^{-5} N - s / m ^{2}$. If this particle is moving with a uniform horizontal speed of $0.02\, m / s$, the number of excess electrons on the drop are $6 k$. The value of $k$ is____

Answer 1

As particle is moving horizontally, only forces acting on it are Stoke's force and electric force.
If $v=$ constant, then $6 \pi \eta r v=q E$
$\Rightarrow 6 \pi \eta r v=n e E $
$\Rightarrow n=\frac{6 \pi \eta r v}{E e}$
$ =\frac{6 \times 3.14 \times 1.6 \times 10^{-5} \times 5 \times 10^{-7} \times 0.02}{6.28 \times 10^{5} \times 1.6 \times 10^{-19}}=30=6 k$
$\Rightarrow k=5$