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Question

Two identical spheres having charges 8μC and 4μC are kept at a certain distance apart. Now they are brought into contact, after that again they are kept at the same distance. Compare the forces in the two cases

A
4:1
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B
12:1
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C
8:1
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D
16:1
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Solution

The correct option is C 8:1
If two identical sphere having charge 8μC and 4μC are kept a certain distance apart, then force between them is F.
Let the distance between charged sphere is d.
then, F=k×8×(4)×1012d2 [attractive]
d2=32k×1012F ....(i)

Now, when both the identical sphere touch, then charge on each sphere is average of initial charge on sphere.
i.e, Q=(84)μC2=2μC on each sphere.
Now, Force between them is:
F=k×(2×106)2d2
From equation (i), we get
F=k×4×1012×F32k×1012
F=F8
so, the ratio is 8:1



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