NTA Abhyas JEE Main2020PhysicsElectrostaticsPractice

A conducting bubble of radius a and thickness t ( t < < a ) has potential V . Now, the bubble collapses into a droplet. The potential of the droplet is

Options

AV ' = V a 3 t 1 3
BV ' = V a 3 t 1 2
CV ' = V a 3 t
DNone of these

Correct answer

A. V ' = V a 3 t 1 3

Step-by-step solution

Let q be the charge on the bubble, then V = Kq a (Here K = 1 4 π ε 0 ) ∴ q = Va K Let after collapsing, the radius of droplet becomes R. Then equating the volume, we have 4 π a 2 t = 4 3 π R 3 ∴ R = 3 a 2 t 1 / 3 Now, potential of droplet will be V ′ = Kq R Substituting the values, we have V ′ = K Va K 3 a 2 t 1 / 3 or V ′ = V a 3 t 1 / 3

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