ઉગમ બિંદુથી \(x-\) અક્ષ પર ત્રણ વિદ્યુતભારો \(+Q, q\) અને \(+Q \) અનુક્રમે \(0,\frac d2\) અને \(d\) આગળ મુકેલ છે. જો \(x=0\) આગળ મુકેલ \(+Q\) દ્વારા અનુભવાતું કુલ બળ શૂન્ય હોય તો \(q\) નું મૂલ્ય કેટલું હશે.

A \(-\frac Q2\)
B \(+\frac Q2\)
C \(+\frac Q4\)
D \(-\frac Q4\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(-\frac Q4\)

Step-by-step Solution

Detailed explanation

For equilibrium, \(\vec{F}_{a}+\vec{F}_{B}=0\) \(\vec{F}_{a}=-\overrightarrow{F_{B}}\) \(\frac{k Q Q}{d^{2}}=-\frac{k Q q}{(d / 2)^{2}}\) \(\Rightarrow q=-\frac{Q}{4}\)

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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