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Question

Two point charges placed at a distance r in air expert a force F on each other. The value of distance R at which they experience force 4F when placed in a medium of dielectric constant K=16 is:

A
r
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B
r4
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C
r8
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D
2r
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Solution

The correct option is C r8
Two points charge placed at a distance =r
force =F
value of distance =R
F=14πϵ0q1q2r2
4F=14πϵ0×Kq1q2R2
or, F=14πϵ0×4×16×q1q2R2
or, 14πϵ0q1q2r2 =16414πϵ0q1q2R2
=164(14πϵ0q1q2R2)
or, 1r2=164×(14πϵ0q1q2R2)
or, 1r2=164×1R2
1r=181R
or, R=r8

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