## College Physics (4th Edition)

After the spheres are separated, the smaller sphere will have a charge of $4.8~\mu C$ and the larger sphere will have a charge of $19.2~\mu C$
When the two spheres are brought in contact, the charges will rearrange themselves so there is an equal charge density on each sphere. Let $q_1$ be the final charge on the smaller sphere and let $q_2$ be the final charge on the larger sphere. $\frac{q_1}{A_1} = \frac{q_2}{A_2}$ $\frac{q_1}{\pi~r_1^2} = \frac{q_2}{\pi~r_2^2}$ $q_1 = \frac{q_2~r_1^2}{r_2^2}$ $q_1 = \frac{q_2~r_1^2}{(2r_1)^2}$ $q_1 = \frac{q_2}{4}$ $q_2 = 4~q_1$ We can find $q_1$: $q_1+q_2 = 6.0~\mu C+ 18.0~\mu C$ $q_1+4q_1 = 24.0~\mu C$ $q_1 = \frac{24.0~\mu C}{5}$ $q_1 = 4.8~\mu C$ Then: $~q_2 = (4)(4.8~\mu C) = 19.2~\mu C$ After the spheres are separated, the smaller sphere will have a charge of $4.8~\mu C$ and the larger sphere will have a charge of $19.2~\mu C$