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Question

# In each situation of column-I, some charge distributions are given with all details explained. The electrostatic potential energy and its nature is given situation in column -II. Match the proper entries from column-II to column-I using the codes given below the columns, Column-I Column-II (P) A thin shell of radius a and having a charge −Q uniformly distributed over its surface as shown (1) 18πϵ0Q2a in magnitude (Q) A thin shell of radius 5a2 and having a charge −Q uniformly distributed over its surface and a point charge −Q is brought from infinity and placed at its centre as shown. (2) 320πϵ0Q2a in magnitude (R) A solid sphere of radius a and having a charge −Q uniformly distributed throughout its volume as shown. (3) 27Q80πϵ0Q2a in magnitude (S) A solid sphere of radius a and having a charge −Q uniformly distributed throughout its volume. The solid sphere is surrounded by a concentric thin uniformly charged spherical shell of radius 2a and carrying charge −Q as shown (4) 527πϵ0Q2a in magnitude

A
p1, Q2, R2, S3
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B
p4, Q1, R2, S3
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C
p1, Q2, R3, S1
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D
p2, Q4, R3, S1
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Solution

## The correct option is A p→1, Q→2, R→2, S→3(A) Electrostatic potential energy=14πϵ0−Q22a=14πϵ0(−Q)22a=Q28πϵ0a (B) Electrostatic potential energy=14πϵ0[−Q×(−Q)5a/2+(−Q)22(5a/2)]=320Q2πϵ0a (C) Electrostatic potential energy=14πϵ03Q25a=320Q2πϵ0a (D) Electrostatic potential energy=14πϵ0[3Q25a+(−Q)22(2a)+(−Q)×(−Q)2a]=27Q280πϵ0a

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