A) \[F\]
B) \[\frac{3}{5}F\]
C) \[\frac{4}{9}F\]
D) \[\frac{F}{4}\]
E) \[\frac{F}{2}\]
Correct Answer: D
Solution :
From Coulombs law the force (F) between two charges is \[F=\frac{1}{4\pi {{\varepsilon }_{0}}k}\frac{{{q}^{2}}}{{{r}^{2}}}\] First case: \[k=1\] \[F=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{{{q}^{2}}}{{{r}^{2}}}\] Second case: \[k=4\] \[F=\frac{1}{4\pi {{\varepsilon }_{0}}\times 4}.\frac{{{q}^{2}}}{{{r}^{2}}}\] ?. (2) \[\Rightarrow \] \[\frac{F}{F}=4\] \[\Rightarrow \] \[F=\frac{F}{4}\]
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