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 $0.02m/s$, the number of excess electrons on the drop are $6k$. The value of $k$ is____

Answer 1

Answer: 5

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