એક સમાન રીતે વિદ્યુતભારિત વર્તુળાકાર ગૂંચળાનો વિચાર કરો, જેની ત્રિજ્યા \(\mathrm{a} \sqrt{2}\) છે. કાર્તેઝીયન યામ પદ્ધતિમાં ધન z-અક્ષ પરનું એવું સ્થાન શોધો જ્યાં વિદ્યુતક્ષેત્ર મહત્તમ હોય, જો વલયને xy-સમતલમાં ઉગમબિંદુ પર મૂકેલું ધારી લેવામાં આવે :

A \(\frac{a}{\sqrt{2}}\)
B \(\frac{a}{2}\)
C a
D 0

Verified Solution

Answer & Solution

Correct Answer

(C) a

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & \mathrm{E}=\frac{\mathrm{KQr}}{\left(\mathrm{x}^2+\mathrm{R}^2\right)^{3 / 2}} \\ & \frac{\mathrm{dE}}{\mathrm{dx}}=0 \\ & \therefore \mathrm{x}=\frac{\mathrm{R}}{\sqrt{2}}=\frac{\sqrt{2} \mathrm{a}}{\sqrt{2}}=\mathrm{a}\end{aligned}\)

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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