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Q.

Three equal charges q₁, q₂, q₃ are placed at the three corners ABC of a square ABCD. If the force between the charges at A and B (on q₁ and q₂) is F₁₂ and that between A and C is F₁₃ , then the ratio of magnitudes F₁₂and F₁₃ is

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a

2

b

$\frac{1}{\frac{1}{\sqrt{2}}}$

c

$\frac{1}{2}$

d

$\sqrt{2}$

answer is B.

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Detailed Solution

$Given: q_{1} = q_{2} = q_{3} = q$

$F_{12} \propto \frac{q_{1} q_{2}}{r^{2}} \propto \frac{q^{2}}{r^{2}}$

$F_{13} \propto \frac{q_{1} q_{3}}{(\sqrt{2 r})^{2}} \propto \frac{q^{2}}{2 r^{2}}$

$\Rightarrow \frac{F_{12}}{F_{13}} = \frac{(\frac{q^{2}}{r^{2}})}{(\frac{q^{2}}{2 r^{2}})} = 2$

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Three equal charges q1, q2, q3 are placed at the three corners ABC of a square ABCD. If the force between the charges at A and B (on q1 and q2) is F12 and that between A and C is F13 , then the ratio of magnitudes F12 and F13 is