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Q.

In each situation of column-I, some charge distributions are given with all details explained in column -II The electrostatic potential energy and its nature is given situation in column -II. Then match situation in column-I with the corresponding results in column-II and indicate your answer by darkening appropriate bubbles in the 4×4 matrix given in the OMR..

 Column-I Column-II
A)

A thin shell of radius a and having a charge Q uniformly distributed over its surface as shown

Question Image
P)18π0Q2a in magnitude
B)

A thin shell of radius 5a2 and having a charge Q uniformly distributed over its surface and a point charge Q placed at its centre as shown.

Question Image
Q)320π0Q2a  in magnitude
C)

A solid sphere of radius a and having a charge Q uniformly distributed throughout its volume as shown.

Question Image
R)25π0Q2a  in magnitude
D)

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

Question Image
S)Positive in sign

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a

A-PS,B-QS,C-QS,D-S

b

A-S,B-QS,C-QS,D-PS

c

A-QS,B-PS,C-QS,D-S

d

A-PS,B-QS,C-S,D- QS

answer is B.

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Detailed Solution

(A) Electrostatic potential energy  =14π0(Q)22a=Q28π0a
(B) Electrostatic potential energy 
 =14π0[(Q)×(Q)5a/2+(Q)22(5a/2)]=320Q2π0a
(C) Electrostatic potential energy  =14π03Q25a=320Q2π0a
(D) Electrostatic potential energy 
 =14π0[3Q25a+(Q)22(2a)+(Q)×(Q)2a]=27Q280π0a

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In each situation of column-I, some charge distributions are given with all details explained in column -II The electrostatic potential energy and its nature is given situation in column -II. Then match situation in column-I with the corresponding results in column-II and indicate your answer by darkening appropriate bubbles in the 4×4 matrix given in the OMR.. Column-I Column-IIA)A thin shell of radius a and having a charge Q uniformly distributed over its surface as shownP)18π∈0Q2a in magnitudeB)A thin shell of radius 5a2 and having a charge Q uniformly distributed over its surface and a point charge Q placed at its centre as shown.Q)320π∈0Q2a  in magnitudeC)A solid sphere of radius a and having a charge Q uniformly distributed throughout its volume as shown.R)25π∈0Q2a  in magnitudeD)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 shownS)Positive in sign