Two small identical conducting spheres are placed with their centers 0.32 m apart. One is given a charge of 12 ✕ 10-9 C, the other a charge of - 17 ✕ 10-9 C. (a) Find the electrostatic force exerted on one sphere by the other. magnitude N direction (b) The spheres are connected by a conducting wire. Find the electrostatic force between the two after equilibrium is reached, where both spheres have the same charge. magnitude N direction

(a) - 1.79 x 10⁻⁵ N

(b) 5.49 x 10⁻⁷ N

Explanation:

given information:

r = 0.32 m

q₁ = 12 x 10⁻⁹ C

q₂ = - 17 x 10⁻⁹ C

(a) Find the electrostatic force exerted on one sphere by the other. magnitude N direction

F = k q₁q₂/r²

= (9 x 10⁹) (12 x 10⁻⁹) (-17 x 10⁻⁹) / (0.32) ²

= - 1.79 x 10⁻⁵ N

(b) The spheres are connected by a conducting wire. Find the electrostatic force between the two after equilibrium is reached, where both spheres have the same charge. magnitude N direction

F = kQ²/r²,

where

Q = (q₁+q₂/2)

= (12 + (-17)) x 10⁻⁹/2

= 2.5 x 10⁻⁹ C

thus,

F = (9 x 10⁹) (2.5 x 10⁻⁹) ² / (0.32) ²

= 5.49 x 10⁻⁷ N