Question

Two spheres of radius $5cm$ and $10cm$, both charged to $120\mu C$, are joined by a metal wire and then metal wire is removed. What is the charge on each after removal of the wire?

• A. $120\mu C,120\mu C$
• B. $80\mu C,160\mu C$
• C. $100\mu C,140\mu C$
• D. None of these

Answer 1

The correct option is B $80\mu C,160\mu C$

When they are joined by wire, Potential of the system is $V=k\frac{Q_1+Q_2}{r_1+r_2}$.

When wire is removed , potential of each sphere - $V_1^{\prime }=k\frac{Q_1^{\prime }}{r_1}$ and $V_2^{\prime }=k\frac{Q_2^{\prime }}{r_2}$

Just after removal wire , $V=V_1^{\prime }=V_2^{\prime }$

thus, $Q_1^{\prime }=\frac{(Q_1+Q_2)r_1}{r_1+r_2}=\frac{(120+120)5}{10+5}=80\mu C$

$Q_2^{\prime }=\frac{(Q_1+Q_2)r_2}{r_1+r_2}=\frac{(120+120)10}{10+5}=160\mu C$