\(Q\) જેટલો વિદ્યુતભાર ધરાવતા બે બિંદુવત્ત વીજભારોને \(d\) જેટલા અંતરે રાખવામાં આવ્યા છે. \(q\) જેટલા બિંદુવત્ત ત્રીજા વિદ્યુતભારને લંબ દ્વિભાજક પર મધ્ય બિંદુ થી \(x\) અંતરે છે \(q\) પર મહત્તમ કુલંબબળ અનુભવે તે \(x\) નું મૂલ્ય ............ હશે.

A \(x=d\)
B \(x=\frac{d}{2}\)
C \(x=\frac{d}{\sqrt{2}}\)
D \(x=\frac{d}{2 \sqrt{2}}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(x=\frac{d}{2 \sqrt{2}}\)

Step-by-step Solution

Detailed explanation

\(F =\frac{ KQq }{\left( x ^{2}+\frac{ d ^{2}}{4}\right)}\) Net force on \(g =2 F \cos \theta\) \(F _{\text {act }}=\frac{2 KQqx }{\left( x ^{2}+\frac{ d ^{2}}{4}\right)^{3 / 2}}\) For maximum \(F _{\text {act }}\) \(\frac{ d F _{\text {net }}}{ dx }=0\) we get…

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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