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Question

Three concentric conducting spherical shells of radii R,2R and 3R carry charges Q,2Q and 3Q, respectively. Compute the potential at r=R, and the charges on the spheres of radii R and 3R.
222113_295d4e02a2df4a38b2617fedd8dc55c2.png

A
Q+2Q112πε0R,Q1=Q4,Q2=7Q2
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B
Q+2Q112πε0R,Q1=Q2,Q2=7Q2
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C
Q+2Q112πε0R,Q1=Q2,Q2=7Q4
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D
Q+2Q112πε0R,Q1=Q4,Q2=7Q4
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Solution

The correct option is B Q+2Q112πε0R,Q1=Q2,Q2=7Q2
Let A has charge Q1 and C has charge Q2. After getting connected:
VA=VC
14πϵ0[Q1R+2Q2R+Q23R]=14πϵ0[Q13R2Q3R+Q23R]
Q12Q+Q23=Q132Q3+Q23
Q1=Q2
Now, Q1+Q2=4QQ2=7Q2

Using Q1 and Q2 potential will be:
=14πϵ0[Q1R+2Q2R+Q23R]
=Q+2Q112πϵ0R


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