There are two equally charged identical metal spheres A and B repel each other with a force 3$\times$10^-5 N. Another identical uncharged sphere C is touched with A and then placed at the mid-point between A and B. Net force on C is

If same charges on spheres A and Bare q, then force,

             $\mathrm{F}=\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{{\mathrm{q}}^2}{{\mathrm{r}}^2}=3\times {10}^{-5}\mathrm{N}$

Charge on A and C after touching,

              ${\mathrm{q}}_{\mathrm{A}}^{\mathrm{\prime }}={\mathrm{q}}_{\mathrm{C}}=\frac{\mathrm{q}}{2}$

Net force on C,

$\begin{array}{c}\mathbf{F}={\mathbf{F}}_{\mathrm{A}}+{\mathbf{F}}_{\mathrm{B}}\\ \therefore \mathrm{F}=\left|\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{(\mathrm{q}/2)(\mathrm{q}/2)}{(\mathrm{r}/2{)}^2}-\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{(\mathrm{q}/2)\times \mathrm{q}}{(\mathrm{r}/2{)}^2}\right|\\ =\left|\frac{1}{4{\mathrm{\pi \epsilon }}_0\mathrm{r}}\frac{{\mathrm{q}}^2}{{\mathrm{r}}^2}-2\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{{\mathrm{q}}^2}{{\mathrm{r}}^2}\right|\\ =\left|-\left(\frac{1}{4{\mathrm{\pi \epsilon }}_0}\cdot \frac{\mathrm{q}}{{\mathrm{r}}^2}\right)\right|=3\times {10}^{-5}\mathrm{N}\end{array}$