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When n identical mercury droplets charged to the same potential V coalescence to form a single bigger drop. The potential of the new drop will be
- a)V/n
- b)n2/3V
- c)nV2
- d)nV
Correct answer is option 'B'. Can you explain this answer?
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Explanation:
Principle of Conservation of Charge:
- According to the principle of conservation of charge, the total charge before and after the coalescence of droplets remains the same.
- If n identical droplets coalesce to form a single bigger drop, the total charge remains constant.
Relationship between Potential and Charge:
- The potential of a charged droplet is directly proportional to its charge.
- Let Q be the charge of each droplet. Therefore, the total charge before coalescence is nQ.
Calculation of Potential of the New Drop:
- After coalescence, the total charge is still nQ, but it is now distributed in a single bigger drop.
- Let V' be the potential of the new drop. According to the given options, we need to determine the relationship between V and V'.
- As the total charge remains the same, the potential of the new drop can be calculated as V' = nQ/C, where C is the capacitance of the new drop.
- The capacitance of a sphere is given by C = 4πε₀r, where r is the radius of the sphere.
- Since the droplets coalesce to form a bigger drop, the radius of the new drop is related to the number of droplets n. The relationship between the radius of the new drop and the number of droplets n is r ∝ n^(1/3).
- Substituting the values, we get V' = nQ/(4πε₀r) = nQ/(4πε₀r ∝ nQ/(4πε₀n^(1/3)) = n^(2/3)V.
Therefore, the potential of the new drop is given by V' = n^(2/3)V, which corresponds to option (b).
Principle of Conservation of Charge:
- According to the principle of conservation of charge, the total charge before and after the coalescence of droplets remains the same.
- If n identical droplets coalesce to form a single bigger drop, the total charge remains constant.
Relationship between Potential and Charge:
- The potential of a charged droplet is directly proportional to its charge.
- Let Q be the charge of each droplet. Therefore, the total charge before coalescence is nQ.
Calculation of Potential of the New Drop:
- After coalescence, the total charge is still nQ, but it is now distributed in a single bigger drop.
- Let V' be the potential of the new drop. According to the given options, we need to determine the relationship between V and V'.
- As the total charge remains the same, the potential of the new drop can be calculated as V' = nQ/C, where C is the capacitance of the new drop.
- The capacitance of a sphere is given by C = 4πε₀r, where r is the radius of the sphere.
- Since the droplets coalesce to form a bigger drop, the radius of the new drop is related to the number of droplets n. The relationship between the radius of the new drop and the number of droplets n is r ∝ n^(1/3).
- Substituting the values, we get V' = nQ/(4πε₀r) = nQ/(4πε₀r ∝ nQ/(4πε₀n^(1/3)) = n^(2/3)V.
Therefore, the potential of the new drop is given by V' = n^(2/3)V, which corresponds to option (b).
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When n identical mercury droplets charged to the same potential V coalescence to form a single bigger drop. The potential of the new drop will bea)V/nb)n2/3Vc)nV2d)nVCorrect answer is option 'B'. Can you explain this answer?
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