Question

Two charged metal spheres A and B have radii in the ratio 2:3 with charges $5\times {10}^{-6}C$ and $10\times {10}^{-6}C$ respectively. If they are connected by a wire. Then

• A. 5μC of charge flows from B to A till their charges are equal
• B. 1μC of charge flows from A to B till common potential is reached
  
• C. 1μC of charge flows from B to A till common potential is reached
  
• D. No charge flows between A and B

Answer 1

The correct option is C 1μC of charge flows from B to A till common potential is reached

$\frac{r_A}{r_B}=\frac{2}{3}\Rightarrow \frac{C_1}{C_2}=\frac{2}{3}$

$\frac{q}{C_1}=\frac{Q-q}{C_2}\Rightarrow q=\frac{C_1}{C_2}(Q-q)\Rightarrow q=\frac{2}{3}(Q-q)$

$\Rightarrow \frac{5q}{3}=\frac{2Q}{3}\Rightarrow q=\frac{2}{5}Q=\frac{2}{5}\times 15\times {10}^{-6}\Rightarrow q=6\times {10}^{-6}C$

$1\mu C$ charge flows from B to A till common potentials is reached.