સમાન મૂલ્યના ત્રણ વિધુતભારો ચોરસનાં ત્રણ શિરોબિંદુઓ પર મૂકેલાં છે. જો \(q_1\) અને\(q_2\) વચ્ચે લાગતું કુલંબ બળ\(F_{12}\) હોય અને \(q_1\) અને \(q_3\)વચ્ચે લાગતું કુલંબ બળ\(F _{13}\) હોય, તો \(\frac{F_{13}}{F_{12}}\)= _________.

A \(\frac{1}{2}\)
B 2
C \(\frac{1}{\sqrt{2}}\)
D \(\sqrt{2}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{1}{2}\)

Step-by-step Solution

Detailed explanation

(A)

\(q_1\) અને \(q_2\) વચ્યે લાગતું કુલંબ બળ
\(F _{12}=\frac{k q_1 q_2}{r^2}=\frac{k q^2}{r^2}\)
\(q_1\) અને \(q_3\) વચ્ચે લાગતું કુલંબ બળ
\(\begin{array}{l} F _{13}=\frac{k q_1 q_3}{r^2} \\ F_{13}=\frac{k q^2}{(\sqrt{2} r)^2} \quad(\because r=\sqrt{2} r) \\ F _{13}=\frac{k q^2}{2 r^2} \\ \frac{F_{13}}{F_{12}}=\frac{k q^2}{2 r^2} \times \frac{r^2}{k q^2}=\frac{1}{2}\end{array}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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