Question
Two metal plates ( $A,B$ ) are kept horizontally with separation of $\left( \frac{12}{\pi} \right)cm$, with plate A on the top. An atomizer jet sprays oil (density $1.5\text{ }g/{cm}^{3}$ ) droplets of radius 1 mm horizontally. All oil droplets carry a charge 5 nC . The potentials $V_{A}$ and $V_{B}$ are required on plates A and B respectively in order to ensure the droplets do not descend. The values of $V_{A}$ and $V_{B}$ are $\_\_\_\_$ .
(Neglect the air resistance to the droplets and take $g = 10\text{ }m/s^{2}$ )
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Solution
Sol. [Key Concept: Balance $qE = mg$ with $E = \Delta\ V/d$ and $m = \frac{4}{3}\pi\ r^{3}\rho$.]
$${\frac{\Delta V}{(12/\pi) \times 10^{- 2}} \times 5 \times 10^{- 9} = \frac{4}{3}\pi\left( r^{3} \right)\rho(g) }{\Delta V \times 5 \times 10^{- 7} = 16\left( r^{3} \right)\rho(g) }{\Delta V = 480,{\text{ }V}_{A} < V_{B} }$$Plate A will be lower potential.
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