આકૃતિમાં દર્શાવ્યા પ્રમાણે બે બિંદુવત વિજભાર \(+Q\) અને \(-Q\) ને એક ગોળીય કવચની બખોલમાં મૂકેલા છે. વિજભારને બખોલની સપાટીની નજીક અને કેન્દ્રથી વિરુદ્ધ દિશામાં મૂકેલા છે. જો \(\sigma _1\) એ અંદરની સપાટી પૃષ્ઠ વિજભારઘનતા અને \(Q_1\) તેના પર રહેલો કુલ વિજભાર અને \(\sigma _2\) એ બહારની સપાટીની પૃષ્ઠ વિજભારઘનતા અને \(Q_2\) તેના પર રહેલો કુલ વિજભાર હોય તો ...

A \(\begin{array}{l} {\sigma _1}\, \ne \,0,\,\,{Q_1}\, = \,0\\ {\sigma _2}\, = \,0,\,\,{Q_2}\, = \,0 \end{array}\)
B \(\begin{array}{l} {\sigma _1}\, \ne \,0,\,\,{Q_1}\, = \,0\\ {\sigma _2}\, \ne \,0,\,\,{Q_2}\, = \,0 \end{array}\)
C \(\begin{array}{l} {\sigma _1}\, = \,0,\,\,{Q_1}\, = \,0\\ {\sigma _2}\, = \,0,\,\,{Q_2}\, = \,0 \end{array}\)
D \(\begin{array}{l} {\sigma _1}\, \ne \,0,\,\,{Q_1}\, \ne \,0\\ {\sigma _2}\, \ne \,0,\,\,{Q_2}\, \ne \,0 \end{array}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(\begin{array}{l} {\sigma _1}\, = \,0,\,\,{Q_1}\, = \,0\\ {\sigma _2}\, = \,0,\,\,{Q_2}\, = \,0 \end{array}\)

Step-by-step Solution

Detailed explanation

Inside the cavity net charge is zero. \(\therefore \quad Q_{1}=0\) and \(\sigma_{1}=0\) There is no effect of point charges \(+Q\) \(Q\) and induced charge on inner surface on the outer surface. \(\therefore \quad Q_{2}=0\) and \(\sigma_{2}=0\)

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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