Two metal spheres, each of radius 3.0 cm, have a center-to center separation of2.0 m. Sphere 1 has charge `+1.0 xx 10^(-8) C,` sphere 2 has charge `-8.0 xx 10^(-8) C`. Assume that the separation is large enough for us to say that the charge on each sphere is uniformly distributed (the spheres do not affect each other). With `V=0` at infinity, calculate (a) the potential at the point halfway between the centers and the potential on the surface of (b) sphere 1 and ( c) sphere 2.

Explanation

To solve the problem, we will calculate the electric potential at three different points: (a) halfway between the centers of the two spheres, (b) on the surface of sphere 1, and (c) on the surface of sphere 2.

### Given Data:
- Radius of each sphere, \( r = 3.0 \, \text{cm} = 0.03 \, \text{m} \)
- Center-to-center separation, \( d = 2.0 \, \text{m} \)
- Charge on sphere 1, \( Q_1 = +1.0 \times 10^{-8} \, \text{C} \)
- Charge on sphere 2, \( Q_2 = -8.0 \times 10^{-8} \, \text{C} \)
- Coulomb's constant, \( k = 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \)
...