A point dipole lies at the origin with its dipole moment along x-axis. A point charge when placed at (3a, 0, 0) and (a, 0, 0) experiences forces due to dipole with respective magnitudes of $F_{1}$ and $F_{2}$ .Then $\frac{F_{2}}{F_{1}} =$

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$\frac{1}{27}$

$\frac{1}{9}$

answer is A.

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Detailed Solution

Along the axial line, electric field due to dipole is:

$E_{θ} = 0$ and $E_{r} \propto \frac{1}{r^{3}}$

$\Rightarrow F_{θ} = 0$ and $F_{r} \propto \frac{1}{r^{3}}$

$\Rightarrow \frac{F_{2}}{F_{1}} = \frac{r_{1}^{3}}{r_{2}^{3}} = \frac{{(3 a)}^{3}}{a^{3}} = 27$

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