Three equal point charges, each with charge 1.30 μC , are placed at the vertices of an equilateral triangle whose sides are of length 0.400 m .
1. What is the electric potential energy U of the system? (Take as zero the potential energy of the three charges when they are infinitely far apart.) Use ϵ0 = 8.85 x 10^−12 C^2N*m^2 for the permittivity of free space.

Respuesta :

Explanation:

The given magnitude of three point charges is as follows.

       [tex]q_{1} = q_{2} = q_{3} = q[/tex]

where,   q = [tex]1.30 \times 10^{-6} C[/tex]      (as [tex]1 \mu C = 10^{-6} C[/tex])

Length of the side is represented as d = 0.4 m

Let U be the electric potential energy of the system and it is represented as follows.

             U = [tex]U_{12} + U_{13} + U_{23}[/tex]

                 = [tex]\frac{1}{4 \pi \epsilon_{o}} \frac{3q^{2}}{d}[/tex]

                 = [tex]\frac{8.99 \times 10^{9} Nm^{2}/C^{2} \times 3 \times (1.30 \times 10^{-6})^{2}}{0.4}[/tex]

                 = [tex]11.39 \times 10^{-2}[/tex] J

Thus, we can conclude that the electric potential energy U of the given system is [tex]11.39 \times 10^{-2}[/tex] J.