Three equal point charges, each with charge 1.40 μCμC , are placed at the vertices of an equilateral triangle whose sides are of length 0.300 mm . What is the electric potential energy UUU of the system? (Take as zero the potential energy of the three charges when they are infinitely far apart.) Use ϵ0ϵ0epsilon_0 = 8.85×10−12 C2N⋅m2C2N⋅m2 for the permittivity of free space.

U_total = 3.51 10⁻¹ J

Explanation:

The electic potential energy is

      U = ∑ k qi qj / rij

Where k is the Coulomb constant 8.988 109 N m² / C², q are the electric charges and r is the distance between them

Let's apply this equation to our case

    Total U = U₁₂ + U₁₃ + U₂₃

The distance between them is the length of the triangle L= 0.3 m, the charge are equal q = 1.40 10⁻⁶ C

       U₁₂ = k q₂ / L

All energies are equal for this case, we substitute in the total potential energy

     U_total = 3 (k q² / L)

     U_total = 6 k q² / L

We calculate

     U_total = 6 8,988 10⁹ (1.40 10⁻⁶)² / 0.3

     U_total = 3.51 10⁻¹ J

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