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Two metal spheres, one of radius R and the other of radius 2R, both have the same surface density σ. If they are brought in contact and separated, then the new surface charge densities on each of the sphere are respectively
- a)
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two metal spheres, one of radius R and the other of radius 2R, both ha...
Before contact, Charges of each sphered,
q1 = σ4πR2; q2 = σ4π(2R)2 = 4q1
When the two sphere are brought in contact, their charges are shared till their potentials become equal i.e., V1 = V2
∴ q2′ = 2q1′....(i)
As there is no loss of charge in the process
∴ q1′ + q2′ = q1 + q2 = q1 + 4q1 = 5q1 = 5(σ4πR2)
or q1′ + 2q1′ = 5σ4πR2 (using (i))
q1 = σ4πR2; q2 = σ4π(2R)2 = 4q1
When the two sphere are brought in contact, their charges are shared till their potentials become equal i.e., V1 = V2
∴ q2′ = 2q1′....(i)
As there is no loss of charge in the process
∴ q1′ + q2′ = q1 + q2 = q1 + 4q1 = 5q1 = 5(σ4πR2)
or q1′ + 2q1′ = 5σ4πR2 (using (i))
Most Upvoted Answer
Two metal spheres, one of radius R and the other of radius 2R, both ha...
Before contact, Charges of each sphered,
q1 = σ4πR2; q2 = σ4π(2R)2 = 4q1
When the two sphere are brought in contact, their charges are shared till their potentials become equal i.e., V1 = V2
∴ q2′ = 2q1′....(i)
As there is no loss of charge in the process
∴ q1′ + q2′ = q1 + q2 = q1 + 4q1 = 5q1 = 5(σ4πR2)
or q1′ + 2q1′ = 5σ4πR2 (using (i))
q1 = σ4πR2; q2 = σ4π(2R)2 = 4q1
When the two sphere are brought in contact, their charges are shared till their potentials become equal i.e., V1 = V2
∴ q2′ = 2q1′....(i)
As there is no loss of charge in the process
∴ q1′ + q2′ = q1 + q2 = q1 + 4q1 = 5q1 = 5(σ4πR2)
or q1′ + 2q1′ = 5σ4πR2 (using (i))
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Two metal spheres, one of radius R and the other of radius 2R, both have the same surface density σ. If they are brought in contact and separated, then the new surface charge densities on each of the sphere are respectivelya)b)c)d)Correct answer is option 'B'. Can you explain this answer?
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