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A conducting sphere of radius 10 cm is charged with 10 μC. Another uncharged sphere of radius 20 cm in allowed to touch it for some time. If both the spheres are separated, then surface density of charges on the spheres will be in the ratio of
  • a)
    1:4
  • b)
    4:1
  • c)
    1:2
  • d)
    2:!
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A conducting sphere of radius 10 cm is charged with 10 μC. Another unc...
When the two conducting spheres touch each other there will be a flow of charge until they both have the same potential.
Let R1 and R2 be the radii of spheres 1 and 2, respectively.  Let Q1 and Q2 be the charges on spheres 1 and 2, respectively, after they are separated. Since both have the same potential,

V = Q1/C1 = Q2/C2
   ⇒ Q1/(4πϵ0R1) = Q2/(4πϵ0R2)
   ⇒ Q1/R1 = Q2/R2
   ⇒  Q1/Q2 = R1/R2
Surface charge density on sphere 1 = σ1 =  Q1/(4πR12)
 Surface charge density on sphere 2 = σ2 = Q2/(4πR22)

σ1 /σ2 = (Q1/Q2) x (R22/R12) 
           =  (R1/R2) x (R22/R12) 
           = R2/R1
           = 20 cm/10 cm
           = 2
Therefore   σ1 : σ2 = 2 : 1

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A conducting sphere of radius 10 cm is charged with 10 μC. Another uncharged sphere of radius 20 cm in allowed to touch it for some time. If both the spheres are separated, then surface density of charges on the spheres will be in the ratio ofa)1:4b)4:1c)1:2d)2:!Correct answer is option 'D'. Can you explain this answer?
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