Question:
Two metal spheres, one of radius R and the other of radius 2R, both have the same surface charge density σ. They are brought in contact and separated. What will be new surface charge densities on them?
Solution:
Following are the charges on the metal sphere before contact
Q1 = σ.4πR2
Q2 = σ.4π(2R)2 = 4Q1
Q1’ and Q2’ are the charges on the metal sphere after contact
Q1’ + Q2’ = Q1 + Q2 = 5Q1
When the metal spheres are in contact, the following is the potentials acquired by them
Q1’ = Q2’/2
Solving the equations we
σ1 = 5 σ/3
σ2 = 5 σ/6
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