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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 p1, Q2, R2, S3
(A) Electrostatic potential energy=14πϵ0Q22a=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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