ત્રણ સમકેન્દ્રિયો ધાતુ કવચો \(A,B\) અને \(C\) ની અનુક્રમે ત્રિજયાઓ \(a,b\) અને \(c\) \(( a < b < c)\) ની પૃષ્ઠ વિદ્યુતભાર ઘનતાઓ અનુક્રમે \( + \sigma , - \sigma \) અને \( + \sigma \) છે. \(B\) કવચનું સ્થિતિમાન :

A \(\frac{\sigma}{\epsilon_0} \left[ {\frac{a^2-b^2}{b}+c} \right ]\)
B \(\frac{\sigma}{\epsilon_0} \left[ {\frac{b^2-c^2}{b}+a} \right ]\)
C \(\frac{\sigma}{\epsilon_0} \left[ {\frac{b^2-c^2}{c}+a} \right ]\)
D \(\frac{\sigma}{\epsilon_0} \left[ {\frac{a^2-b^2}{a}+c} \right ]\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{\sigma}{\epsilon_0} \left[ {\frac{a^2-b^2}{b}+c} \right ]\)

Step-by-step Solution

Detailed explanation

Potential outside the shell, \(V_{outside}\) \(=\frac{\mathrm{KQ}}{\mathrm{r}}\) where \(\mathrm{r}\) is distance of point from the centre of shel Potential inside the shell, \(V_{\text {inside }}=\frac{K Q}{R}\) where \('R"\) is radius of the shell…

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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