Three point charges q1-q - q2-q and q3-Q are placed at points having position vectors r1 - r2 and r1-r2 respectively- It is known that- -r1-r2-r - The net electrostatic force on q3 is -3 times the force applied by either of q1 or q2 on q3- Find r1-r2

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Potential Energy - External Viewpoint

Three point c...

Question

Three point charges $q_{1} = q, q_{2} = q$ and $q_{3} = Q$ are placed at points having position vectors $_{1},_{2}$ and $(_{1} +_{2})$ respectively. It is known that, $|_{1} | = |_{2} | = \to r .$ The net electrostatic force on $q_{3}$ is $\sqrt{3}$ times the force applied by either of $q_{1}$ or $q_{2}$ on $q_{3}$ . Find $_{1} \cdot_{2}$

r^{2}

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\frac{r^{2}}{2}

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\frac{r^{2}}{3}

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\frac{r^{2}}{4}

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Solution

The correct option is B $\frac{r^{2}}{2}$
The positions of three point charges is as shown in the figure below,

From the data given in the question, $F = \sqrt{3} F_{0}$

From the diagram, $|_{1} | = |_{2} | = F_{0} (say)$

Therefore, $\sqrt{{(F_{0})}_{0}^{2} + {(F_{0})}_{0}^{2} + 2 (F_{0}) cos θ} = \sqrt{3} F_{0}$

$\Rightarrow cos θ = \frac{1}{2} \Rightarrow θ = 60^{\circ}$

So, The value of $_{1} \cdot_{2} = r \times r \times cos 60^{\circ} = \frac{r^{2}}{2}$

Hence, option (b) is the correct answer.

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Three point charges q1=q , q2=q and q3=Q are placed at points having position vectors →r1 , →r2 and (→r1+→r2) respectively. It is known that, |→r1|=|→r2|=→r. The net electrostatic force on q3 is √3 times the force applied by either of q1 or q2 on q3. Find →r1⋅→r2