## College Physics (4th Edition)

The ratio of the magnitude of the force on either sphere after they were touched to that before they were touched is $\frac{4}{5}$
We can find the original magnitude of the electric force: $F_1 = \frac{k~\vert q_1 \vert ~\vert q_2 \vert}{L^2}$ $F_1 = \frac{k~(5.0~\mu C)(1.0~\mu C)}{L^2}$ After the two spheres touch, the charge on each sphere is $+2.0~\mu C$ We can find the new magnitude of the electric force: $F_2 = \frac{k~\vert q_1 \vert ~\vert q_2 \vert}{L^2}$ $F_2 = \frac{k~(2.0~\mu C)(2.0~\mu C)}{L^2}$ We can find the ratio $\frac{F_2}{F_1}$: $\frac{F_2}{F_1} = \frac{\frac{k~(2.0~\mu C)(2.0~\mu C)}{L^2}}{\frac{k~(5.0~\mu C)(1.0~\mu C)}{L^2}}$ $\frac{F_2}{F_1} = \frac{(2.0~\mu C)(2.0~\mu C)}{(5.0~\mu C)(1.0~\mu C)}$ $\frac{F_2}{F_1} = \frac{4}{5}$ The ratio of the magnitude of the force on either sphere after they were touched to that before they were touched is $\frac{4}{5}$