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Question

In the given figure, sphere 1 is a conducting sphere while sphere 2 is a non-conducting solid sphere of radius a and b respectively. The distance between centres is d. Find the total energy of the arrangement. (d>>a,d>>b)


A
Q218πε0a+3Q2220πε0bQ1Q24πε0d
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B
Q228πε0a+3Q218πε0bQ1Q28πε0d
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C
Q224πε0a+3Q218πε0bQ1Q28πε0d
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D
None of above
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Solution

The correct option is A Q218πε0a+3Q2220πε0bQ1Q24πε0d
Self electrostatic potential energy of the sphere 1 is,
(Uself)1=Q218πε0a

Self electrostatic potential energy of the sphere 2 is,
(Uself)2=3Q2220πε0b

Energy of the system due interaction between the charges distributed on sphere 1 and 2,

Interaction energy=Q1Q24πε0d

Now,
Total energyUt=(Uself)1+(Uself)2+Interaction energy

Substituting the values,
Ut=Q218πε0a+3Q2220πε0aQ1Q24πε0d

Hence, option (a) is correct answer.

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