Two metal plates (A, B) are kept horizontally with separation of cm, with plate A on the top. An atomizer jet sprays oil

Question

Two metal plates (A, B) are kept horizontally with separation of $(\frac{12}{π})$ cm, with plate A on the top. An atomizer jet sprays oil (density 1.5 ${g/cm}^{3}$ ) 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 $g = 10 {m/s}^{2}$ ) [2026]

Smart Achievers · Accepted Answer

(1)

$m g = q E \Rightarrow V ρ g = q E$

$\frac{4}{3} π r^{3} \cdot ρ \cdot g = q \cdot \frac{(V_{B} - V_{A})}{\frac{12}{π \times 100}}$

$\frac{4}{3} π 10^{- 9} \times \frac{1.5}{10} \times 10^{3} \times 10 = \frac{5 \times 10^{- 9} \times Δ V \times π \times 100}{12}$

$Δ V = 48 \times 10 = 480 V$

Solution

1 100 V and 580 V

2 580 V and 100 V

3 60 V and 400 V

4 0 V and −200 V

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