Question

If the distance between two unlike poles is doubled then the force of attraction between them becomes ______ times its original value.

• A. $0.25$
• B. $0.5$
• C. $0.125$
• D. $2$

Answer 1

The correct option is A $0.25$

Force between two charges at a distance r is

$F=\frac{1}{4\pi {ϵ}_0}\frac{q_1{q}_2}{r^2}$

when r' = 2r

then

$F^{\prime }=\frac{1}{4\pi {ϵ}_0}\frac{q_1{q}_2}{{r^{\prime }}^2}$

$F^{\prime }=\frac{1}{4\pi {ϵ}_0}\frac{q_1{q}_2}{4r^2}$

$F^{\prime }=\frac{1}{4}Fi.e.0.25F$