Two charges of magnitude 5nC and -2nC are placed at points (2cm,0,0) and
(xcm ,0,0) in a region of space, where there is no other external field. If the
electrostatic potential energy of the system is -0.5 µJ, what is the value of
x?

Te electric potential enery U = kq₁q₂/r were q₁ = 5 nC = 5 × 10⁻⁹ C and q₂ = -2 nC = -2 × 10⁻⁹ C and r = √(x - 2)² + (0 - 0)² +(0 - 0)² = x - 2. U = -0.5 µJ = -0.5 × 10⁻⁶ J, k = 9 × 10⁹ Nm²/C².

So r = kq₁q₂/U

x - 2 = kq₁q₂/U

x = 0.02 + kq₁q₂/U m

x = 0.02 + 9 × 10⁹ Nm²/C² × 5 × 10⁻⁹ C × -2 × 10⁻⁹ C/-0.5 × 10⁻⁶ J

x = 0.02 - 90 × 10⁻⁹ Nm²/-0.5 × 10⁻⁶ J

x = 0.02 + 0.18 = 0.2 m = 20 cm

Two charges of magnitude 5nC and -2nC are placed at points (2cm,0,0) and (xcm ,0,0) in a region of space, where there is no other external field. If the electrostatic potential energy of the system is -0.5 µJ, what is the value of x?

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Two charges of magnitude 5nC and -2nC are placed at points (2cm,0,0) and
(xcm ,0,0) in a region of space, where there is no other external field. If the
electrostatic potential energy of the system is -0.5 µJ, what is the value of
x?