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

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