9. Two 6 μC point charges are located at the points (2 m, 0 m) and (0 m, 2 m), and a -3.5 μC charge is at the origin. How much work is required to move these charges an infinite distance away from each other?

-27 mJ

Explanation:

The work done in moving the three charges an infinite distance from each other is the electric potential energy of the system. Let q₁ = q₂ = 6 μC = 6 × 10⁻⁶ C, q₃ =  -3.5 μC = -3.5 × 10⁻⁶ C. Let r₁ be the distance between q₁ and q₃. r₁ = 2 m. Let r₂ be the distance between q₂ and q₃. r₂ = 2 m. Let r₃ be the distance between q₁ and q₂. r₃ = √(2 - 0)² + (0 - 2)² = √4 = 2 m

The potential energy is thus U

U = kq₁q₂/r₃ + kq₁q₃/r₁ + kq₂q₃/r₂

Since q₁ = q₂ = q and r₁ = r₂ = r₃ = r

U = kq(q + 2q₃)/r =

U = 9 × 10⁹ Nm²/C² × 6 × 10⁻⁶ C(6 × 10⁻⁶ C + 2 × -3.5 × 10⁻⁶ C)/2 m

U = 9 × 10⁹ Nm²/C² × 6 × 10⁻⁶ C(6 × 10⁻⁶ C - 7 × 10⁻⁶ C)/2 m

U = 9 × 10⁹ Nm²/C² × 6 × 10⁻⁶ C(- 1 × 10⁻⁶ C)/2 m

U = -54 × 10⁻³ Nm²/2 m

U = -27 × 10⁻³ Nm

U = -27 × 10⁻³ J

U = -27 mJ

So a work of -27 mJ must be done to move the charges an infinite distance away from each other

kinetic

i'm so sorry if this is wrong i'm only in 6th grade xd

it is called kinetic energy