Question

# Two point charges placed at a certain distance r in air exert a force F on each other. The distance r' at which these charges will exert the same force in medium if dielectric constant k is given by

A
r
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B
rk
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C
rk
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D
none of these
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Solution

## The correct option is C r√kTwo point charge placed at a certain distance =rforce =Fdielectric constant =kLet, two point charges q1 and q2 are separated r distance from each other.Then, force experienced between then,F=q1q24πϵ0r2Put, F=q1q24πϵ0r2∴ 4q1q24πϵ0r2=q1q2k(4πϵ0r2)⇒1r2=14r2h⇒1r2=1kr2taking square root both sides 1r−1√kr1or, r1=r√k

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