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There are two small identical metallic s...

There are two small identical metallic spheres A and B each carrying same charge. These two spheres are found to repel each other with a force P. A third identical neutral metal sphere C is first brought in contact with A and then B. The sphere C is taken away from A and B. The magnitude of electric force now is found to be 3F/x. What is x?

Text Solution

Verified by Experts

The correct Answer is:
8
Initially , the force between the charged spheres A and B can be written as :
`F=1/(4piepsilon_0) Q^2/r^2`…(i)
When the sphere C is brought in contact with B then both acquire Q/2 charge . Now when C is brought in contact with B then the charge on both of them becomes `1/2(Q+Q/2 )="3Q"/4` .
The new magnitude of force can be written as follows , according their new magnitudes of charges :
`F=1/(4piepsilon_0) (Q/2 xx"3Q"/4)/r^2 ="3F"/8`
On comparing with the given magnitude of force we can say that x = 8
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