GATE EE 2017 Set 2 — Question 55
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Electromagnetic Fields → Electrostatics → Field & Potential of Charges
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Question
A thin soap bubble of radius , and thickness (), is at a potential of with respect to a reference point at infinity. The bubble bursts and becomes a single spherical drop of soap (assuming all the soap is contained in the drop) of radius . The volume of the soap in the thin bubble is and that of the drop is . The potential in volts, of the resulting single spherical drop with respect to the same reference point at infinity is ________. (Give the answer up to two decimal places.)
Correct answer
9.5 to 10.5
Solution
1.Initial State (Soap Bubble):
The potential of a spherical shell (bubble) of radius and charge is given by:From this, the charge on the bubble is:
2.Conservation of Volume:
The volume of the soap material in the thin bubble is approximately . When it bursts and forms a solid drop of radius , the volume remains the same:3.Final State (Soap Drop):
The charge remains conserved. The potential of the resulting solid drop of radius is:Substituting the value of from step 1:
4.Calculation:
Given and .Now, calculate :
Using the exact value of :
Thus, the potential is approximately , which falls within the range of to .
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