First slide

Electric field

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 $η = 1.6 \times 10^{- 5} N - s / m^{2}$ . If this particle is moving with a uniform horizontal speed of 0.02 m/s, the number of excess electrons on the drop are 6k. The value of k is _________.

Moderate

Solution

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

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