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Two spherical conductors B and C having ...

Two spherical conductors B and C having equal radii and carrying equal charges on them repel each other with a force F when kept apart at some distance. A third spherical conductor having same radius as that B but uncharged is brought in contact with B, then brought in contact with C and finally removed away from both. The new force of repulsion between B and C is

A

`F/4`

B

`(3F)/4`

C

`F/8`

D

`(3F)/8`

Text Solution

Verified by Experts

The correct Answer is:
D
Let the spherical conductors B and C have same charge q. The electric force between them is
`F=1/(4piepsi_(0))(q^(2))/(r^(2))`
r, being the distance between them.
When third uncharged conductor A is brought in contact with B, then charge on each conductor
`q_(A)=q_(B)=(q_(A)+q_(B))/2=(0+q)/2=q/2`
When this conductor A is brought in contact with C, then charge on each conductor
`q_(A)=q_(C)=(q_(A)+q_(C))/2=((q//2)+q)/2=(3q)/4`
Hence, electric force acting between B and C is
`F'=1/(4piepsi_(0))(q_(B)q_(C))/(r^(2))=1/(4piepsi_(0))((q//2)(3q//4))/(r^(2))`
`=3/8[1/(4piepsi_(0))(q^(2))/(r^(2))]=(3F)/8`
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Knowledge Check

  • Two spherical conductors B and C having equal radii and carrying equal charges in them repel each other with a force F when kept apart at some distance. A third spherical conductor having same radius as that of B but uncharged, is brought in contact with B, then brought in contact with C and finally removed away from both. The new force of repulsion between B and C is

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