Consider three identical metal spheres \( \mathrm{A}, \mathrm{B} \)...

Consider three identical metal spheres \( \mathrm{A}, \mathrm{B} \) and \( \mathrm{C} \). Sphere A carries charge \( +6 \mathrm{q} \) and sphere \( \mathrm{B} \) carries charge \( -3 \mathrm{q} \). Sphere \( \mathrm{C} \) carries no charge. Spheres \( \mathrm{A} \) and \( \mathrm{B} \) are touched together and then separated.
Sphere \( \mathrm{C} \) is then touched to sphere \( \mathrm{A} \) and separated from it. Finally the sphere \( \mathrm{C} \) is touched to sphere \( \mathrm{B} \)
P and separated from it. Find the final charge on the sphere \( \mathrm{C} \).