JEE Mains · Physics · STD 12 - 2. Electric potential and capacitance
Two metal plates \((A, B)\) are kept horizontally with separation of \(\left(\dfrac{12}{\pi}\right)\) 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\(^2\))
- A \(100 \, V\) and \(580 \, V\)
- B \(580 \, V\) and \(100 \, V\)
- C \(60 \, V\) and \(400 \, V\)
- D \(0 \, V\) and \(-200 \, V\)
Answer & Solution
Correct Answer
(A) \(100 \, V\) and \(580 \, V\)
Step-by-step Solution
Detailed explanation
For the oil droplets to not descend, the upward electric force must balance the downward gravitational force. \(qE = mg\) The mass of the oil droplet is given by: \(m = \dfrac{4}{3} \pi r^3 \rho\) Substituting the given values \(r = 10^{-3}\) m and \(\rho = 1500\) kg/m\(^3\):…
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