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Two conducting spheres of radii r(1) and...

Two conducting spheres of radii `r_(1)` and `r_(2)` having charges `Q_(1)` and `Q_(2)` respectively are connected to each other. There is

A

no change in the energy of the system

B

an increase in the energy of the system

C

always a decrease in the energy of the system

D

a decrease in the energy of the system unless `Q_(1)r_(2)=Q_(2)r_(1)`

Text Solution

Verified by Experts

The correct Answer is:
D
If potentials of two spheres are same i.e.,
`V_(1)=V_(2)implies(Q_(1))/(4piin_(0)r_(1))=(Q_(2))/(4piin_(0)r_(2))`
`Q_(1)r_(2)=Q_(2)r_(1)`
There will be no redistribution of charge and hence no loss of energy
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[" Two uniformly charged non "],[" conducting spheres of radii "R_(1)" and "],[R_(2)" having charges "Q_(1)" and "Q_(2)],[" respectively are seperated by "],[" distance "r" .Total electrostatic "],[" energy of this system is "],[qquad [U=(1)/(4 pi epsilon_(0)){(3Q_(1)^(2))/(5R_(1))+(3Q_(2)^(2))/(5R_(2))+(Q_(1)Q_(2))/(r)}],[U=(1)/(4 pi epsilon_(0)){(3Q_(1)^(2))/(5R_(1))+(3Q_(2)^(2))/(5R_(2))-(Q_(1)Q_(2))/(r)}],[U=(1)/(4 pi epsilon_(0)){(Q_(1)^(2))/(5R_(1))+(3Q_(2)^(2))/(5R_(2))-(Q_(1)Q_(2))/(r)}],[U=(1)/(4 pi epsilon_(0)){(3Q_(1)^(2))/(5R_(1))+(3Q_(2)^(2))/(R_(2))+(Q_(1)Q_(2))/(r)}]]

Two non-conduction hollow uniformly charged spheres of radil R_(1) and R_(2) with charge Q_(1) and Q_(2) respectively are places at a distance r. Find out total energy of the system.

Knowledge Check

  • The insulated spheres of radii R_(1) and R_(2) having charges Q_(1) and Q_(2) respectively are connected to each other. There is

    A
    No change in the energy of the system
    B
    An increase in the energy of the system
    C
    Always a decrease in the energy of the system
    D
    A decrease in the energy of the system unless
    `Q_(1)R_(2) = Q_(2)R_(1)`

  • Two isolated charged metallic spheres of radii R_(1) and R_(2) having charges Q_(1) and Q_(2) respectively are connected to each other, then there is-

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    No change in the electrical energy of the system
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    An increase in the electrical energy of the system
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  • Two concentric conducting spheres of radii R and 2R are crrying charges Q and -2Q , respectively. If the charge on inner sphere is doubled, the potetial differece between the two spheres will

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    becomes two times
    B
    become four times
    C
    be halved
    D
    remain same

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