$R_{1}$ અને $\mathrm{R}_{2}$ ત્રિજ્યા ધરાવતા બે વિદ્યુતભારિત ગોળાકાર સુવાહકોને એક તારથી જોડવામાં આવેલા છે. તો ગોળાઓની પૃષ્ઠ વિદ્યુતભાર ઘનતાઓનો ગુણોત્તર $\left(\sigma_{1} / \sigma_{2}\right)$ $.....$ છે.

Question

A$\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}$
B$\frac{R_{2}}{R_{1}}$
C$\sqrt{\left(\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}\right)}$
D$\frac{\mathrm{R}_{1}^{2}}{\mathrm{R}_{2}^{2}}$

NEET 2021, Medium

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Solution

b
$\mathrm{Q}_{1}=\frac{\sum \mathrm{Q}}{\mathrm{R}_{1}+\mathrm{R}_{2}} \times \mathrm{R}_{1}$

$\mathrm{Q}_{2}=\frac{\sum Q}{\mathrm{R}_{1}+\mathrm{R}_{2}} \times \mathrm{R}_{2}$

$\sigma_{1}=\frac{\mathrm{Q}_{1}}{4 \pi \mathrm{R}_{1}^{2}}=\frac{\sum Q}{\mathrm{R}_{1}+\mathrm{R}_{2}} \times \frac{\mathrm{R}_{1}}{4 \pi \mathrm{R}_{1}^{2}} \propto \frac{1}{\mathrm{R}_{1}}$

$\sigma_{2}=\frac{\mathrm{Q}_{2}}{4 \pi \mathrm{R}_{2}^{2}}=\frac{\sum Q}{\mathrm{R}_{1}+\mathrm{R}_{2}} \times \frac{\mathrm{R}_{2}}{4 \pi \mathrm{R}_{2}^{2}} \propto \frac{1}{\mathrm{R}_{2}}$

$\frac{\sigma_{1}}{\sigma_{2}}=\frac{\mathrm{R}_{2}}{\mathrm{R}_{1}}$

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