Question

A dust particle of mass \(4 \times 10^{-12} \, {mg}\) is suspended in air under the influence of an electric field of 50 N/C directed vertically upwards. How many electrons were removed from the neutral dust particle? [Take, \(g = 10 \, {m/s}^2\)]

• A. 15
• B. 8
• C. 5
• D. 4

Hint:

The number of electrons removed can be found by balancing the electric force with the gravitational force on the particle.

Answer 1

The Correct Option is C

Step 1: Determine the mass of the dust particle and calculate its weight.
\[m = 4 \times 10^{-12} \, {mg} = 4 \times 10^{-15} \, {kg}\]\[W = mg = 4 \times 10^{-15} \times 10 = 4 \times 10^{-14} \, {N}\]Step 2: Apply the principle of balancing forces to find the charge.
\[qE = W \Rightarrow q = \frac{W}{E} = \frac{4 \times 10^{-14}}{50} = 8 \times 10^{-16} \, {C}\]Step 3: Calculate the number of electrons removed based on the total charge.
\[q = ne \Rightarrow n = \frac{q}{e} = \frac{8 \times 10^{-16}}{1.6 \times 10^{-19}} = 5\]Conclusion: 5 electrons were removed from the neutral dust particle.