Calculate the work required to assemble three charged particles at the vertices of an equilateral triangle, as shown in the figure.

Step-by-step solution

The work required to assemble the system of charges is equal to the electrostatic potential energy of the system. The potential energy U of a system of three point charges is given by: U = 1 4 ₀ ( q₁ q₂ r₁₂ + q₂ q₃ r₂₃ + q₃ q₁ r₃₁ ) Given: q₁ = 2.0 10⁻⁵ C q₂ = 4.0 10⁻⁵ C q₃ = 3.0 10⁻⁵ C r₁₂ = r₂₃ = r₃₁ = 10 cm = 0.1 m 1 4 ₀ = 9 10^9 N m ^2/ C ^2 Substituting the values: U = 9 10^9 0.1 [ (2.0 10⁻⁵)(4.0 10⁻⁵) + (4.0 10⁻⁵)(3.0 10⁻⁵) + (3.0 10⁻⁵)(2.0 10⁻⁵) ] U = 9 10¹⁰ [ 8.0 10⁻¹⁰ + 12.0 10⁻¹⁰ + 6.0 10⁻¹⁰ ] U = 9 10¹⁰