Two metallic charged spheres whose radii are \( 20\text{cm} \) and \( 10\text{cm} \) respectively, have each \( 150\ \mu\text{C} \) positive charge. The common potential after they are connected by a conducting wire is
\( 9 \times 10^6\text{ volts} \)
\( 4.5 \times 10^6\text{ volts} \)
\( 1.8 \times 10^7\text{ volts} \)
\( 13.5 \times 10^6\text{ volts} \)
Solution:
The total charge is \( Q = 150 \mu\text{C} + 150 \mu\text{C} = 300 \mu\text{C} \). The total capacitance is \( C = 4piepsilon_0(R_1 + R_2) = \frac{0.3}{9 \times 10^9}\text{ F} \). The common potential is \( V = \frac{Q}{C} = \frac{300 \times 10^{-6} \times 9 \times 10^9}{0.3} = 9 \times 10^6\text{ V} \).
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