A) \[2\,F\]
B) \[\frac{F}{2}\]
C) \[\frac{F}{4}\]
D) \[\frac{F}{8}\]
Correct Answer: D
Solution :
The electric field at a point distance r from electric dipole is \[E=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{p}{{{r}^{3}}}\] or \[E\propto \frac{1}{{{r}^{3}}}\] where, p is dipole moment and r is distance of point from centre of dipole. Force on that point is \[F=EQ\] or \[F\propto \frac{1}{{{r}^{3}}}\] or \[\frac{{{F}_{2}}}{{{F}_{1}}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{3}}\] or \[\frac{{{F}_{2}}}{{{F}_{1}}}={{\left( \frac{r}{2\,r} \right)}^{3}}\] or \[\frac{{{F}_{2}}}{F}=\frac{1}{8}\] \[\therefore \] \[{{F}_{2}}=\frac{F}{8}\]
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