Three identical charges are placed on three vertices of a square. If the force acting between $q_{1}$ and $q_{2}$ is $F_{12}$ and between $q_{1}$ & $q_{3}$ is $F_{13}$ then $\frac{F_{13}}{F_{12}} =$ ____________.

\frac{1}{2}

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2

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

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\sqrt{2}

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Solution

The correct option is B $\frac{1}{2}$
Let the side of the square be $a$ .
Force acting between charges $q_{1}$ and $q_{2}$ $F_{12} = \frac{k q^{2}}{a^{2}}$
In right angle triangle ABC, $A C^{2} = A B^{2} + B C^{2}$
$⟹ A C^{2} = a^{2} + a^{2} = 2 a^{2}$
$⟹ A C = \sqrt{2} a$
Thus force acting between charges $q_{1}$ and $q_{3}$ $F_{13} = \frac{k q^{2}}{(\sqrt{2} a)^{2}} = \frac{k q^{2}}{2 a^{2}}$
$⟹ \frac{F_{13}}{F_{12}} = \frac{1}{2}$

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Three identical charges are placed on three vertices of a square. If the force acting between q1 and q2 is F12 and between q1 & q3 is F13 then F13F12= ____________.

The correct option is B 12Let the side of the square be a.Force acting between charges q1 and q2 F12=kq2a2In right angle triangle ABC, AC2=AB2+BC2⟹ AC2=a2+a2=2a2⟹ AC=√2aThus force acting between charges q1 and q3 F13=kq2(√2a)2=kq22a2⟹ F13F12=12

Three identical charges are placed on three vertices of a square. If the force acting between $q_{1}$ and $q_{2}$ is $F_{12}$ and between $q_{1}$ & $q_{3}$ is $F_{13}$ then $\frac{F_{13}}{F_{12}} =$ ____________.