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Question

Figure shows three concentric conducting spherical shells with inner and outer shells earthed and the middle shell is given a charge q . Let, q1 be the charge accumulated on sphere 1 and q3 be the charge accumulated on sphere 3, then match the column 1 with column 2 (where, K is Coulomb's constant)

S.No Column 1 S.No Column 2
1. q1 a. 0
2. q3 b. 425q
3. Electrostatic energy of the system stored in the region II. c. 2125q
d. q
e. 2K(q)235r

f. 2K(q1+q)235r

A
1c, 2b, 3e
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B
1b, 2c, 3e
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C
1b, 2c, 3f
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D
1d, 2d, 3a
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Solution

The correct option is C 1b, 2c, 3f
Potential inside an isolated hollow sphere is constant. Concentric hollow sphere potential at a point can be added due to principle of superposition. Grounded Surface will have zero potential.

For sphere 1,
kqr2+kq1r1+kq3r3=0

2q5r+q1r+2q37r=0

14q+35q1+10q3=0 --(1)


For sphere 3,
kq1r3+kqr3+kq3r3=0
q1+q+q3=0 --(2)

From (1) & (2),
q1=425q
& q3=2125q

CII=4πϵ0[(3.5r2.5r)3.5r×2.5r]1=35r4k

UII=(q1+q)22C=2k(q1+q)235r


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