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64 identical drops of mercury are charged simultaneously to the same potential of 10 volts assuming the drops to be spherical if all the charged drops are made to combine to form one large drop then potential will be?
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64 identical drops of mercury are charged simultaneously to the same p...
Answer:
Given Information:
- Number of identical drops of mercury = 64
- Potential of each drop = 10 volts
Determination of Charge of each drop:
- Charge (Q) = Potential (V) x Capacity (C)
- Capacity of a sphere (C) = (4πε₀r)/3, where ε₀ is the permittivity of free space and r is the radius of the sphere.
- Charge of each drop (Q) = 10 x [(4πε₀r)/3]
Determination of Total Charge of 64 drops:
- Total charge (Q) of 64 drops = Charge (Q) x Number of Drops (N)
- Q = 10 x [(4πε₀r)/3]
- N = 64
- Therefore, Total Charge (Q) of 64 drops = 64 x 10 x [(4πε₀r)/3]
Determination of Radius of Combined Drop:
- As the 64 drops are combined to form a single drop, the charge on the drop remains the same.
- Also, the volume of the combined drop is equal to the sum of volumes of all the 64 drops.
- Therefore, [(4/3)πR³] = 64[(4/3)πr³] where R is the radius of the combined drop and r is the radius of each individual drop.
- Solving the above equation, we get R = 4r
Determination of Potential of Combined Drop:
- Potential (V) = Charge (Q) / Capacity (C)
- Capacity of a sphere (C) = (4πε₀r)/3, where ε₀ is the permittivity of free space and r is the radius of the sphere.
- Charge of the combined drop (Q) = Total Charge (Q) of 64 drops
- Therefore, Potential (V) of the combined drop = Total Charge (Q) of 64 drops / [(4πε₀R)/3]
- Substituting the value of R, we get Potential (V) of the combined drop = 10 volts
Conclusion:
The potential of the combined drop is 10 volts. When the 64 identical drops of mercury are made to combine to form one large drop, the potential remains the same as the charge on the drop remains constant and the capacity of the drop increases proportionally to the radius of the combined drop.
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64 identical drops of mercury are charged simultaneously to the same p...
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64 identical drops of mercury are charged simultaneously to the same potential of 10 volts assuming the drops to be spherical if all the charged drops are made to combine to form one large drop then potential will be?
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64 identical drops of mercury are charged simultaneously to the same potential of 10 volts assuming the drops to be spherical if all the charged drops are made to combine to form one large drop then potential will be? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about 64 identical drops of mercury are charged simultaneously to the same potential of 10 volts assuming the drops to be spherical if all the charged drops are made to combine to form one large drop then potential will be? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 64 identical drops of mercury are charged simultaneously to the same potential of 10 volts assuming the drops to be spherical if all the charged drops are made to combine to form one large drop then potential will be?.
64 identical drops of mercury are charged simultaneously to the same potential of 10 volts assuming the drops to be spherical if all the charged drops are made to combine to form one large drop then potential will be? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about 64 identical drops of mercury are charged simultaneously to the same potential of 10 volts assuming the drops to be spherical if all the charged drops are made to combine to form one large drop then potential will be? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 64 identical drops of mercury are charged simultaneously to the same potential of 10 volts assuming the drops to be spherical if all the charged drops are made to combine to form one large drop then potential will be?.
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