Question

Two conducting charge spheres whose radii are 20 cm and 10 cm, respectively have 150 $\mu$C positive charge. The common potential after they have been connected by a conducting wire is :

• A. $9\times {10}^{6}V$
• B. $4.5\times {10}^{6}V$
• C. $1.8\times {10}^{7}V$
• D. $13.6\times {10}^{6}V$

Answer 1

The correct option is A $9\times {10}^{6}V$

Here two spheres are not concentric.
When two sphere are connected by a conducting wire,Let charges be Q1 and Q2.
Q1 + Q2 = $300\mu C$
$\frac{KQ1}{R1}=\frac{KQ2}{R2}$
$Q1=2\times Q2$
$2\times Q2+Q2=300\mu C$
$Q2=100\mu C,Q1=200\mu C$

Common potential is, $V_c=\frac{Q1}{4\pi {ϵ}_0{R}_1}=\frac{200\times {10}^{-6}}{4\times 3.14\times 8.854\times {10}^{-12}\times 20\times {10}^{-2}}\sim 9\times {10}^{6}V$