Charges of `10^(-2)C " and " 5xx 10^(-2)C` are put on two metal spheres of radii 1 cm and 2 cm respectively. If they are connected with a metal wire, what will be the final charge on the smaller sphere ?

Explanation

Here, radius of first sphere, `R_1 = 1cm = 0.01` m and radius of second sphere, `R_2 = 2 cm = 0.02`m.
Capacitance of fisrt sphere, `C_1= 4pi in_0 R_1` and capacitance of second sphere, `C_2= 4pi in_0 R_2`
The total amount of charge before and after connection,
`Q_1+Q_2= Q=(C_1+C_2)V`
`V = (Q_1+Q_2)/(C_1+C_2)`
Final charge on the smaller (first) sphere,
`q_1= C_1V= C_1(Q_1+Q_2)/(C_1+C_2)`
`[" Given ",Q_1= 10^(-2)C " and "Q_2=5xx10^(-2)C]`
`=4pi in_0R_1xx(10^(-2)+5xx10^(-2))/(4pi in_0R_1+4 pi in_0R_2)`
`= R_1xx(6xx10^(-2))/(R_1+R_2) = 0.01xx(6xx10^(-2))/(0.01+0.02)= 0.02C`.