Consider the group of three+2.4 nC point charges shown in the figure.What is the electric potential energy of this system of charges relative to infinity? (k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²) A) 4.1 × 10^-6 J B) 4.6 × 10^-6 J C) 4.2 × 10^-6 J D) 4.4 × 10^-6 J

Question

Quizplus · Accepted Answer

The electric potential energy of a system of charges is given by the formula: U = 1/2 ∑ (qi qj)/4πε0r, where qi and qj are the charges, r is the distance between them, and ε0 is the permittivity of free space.

We can calculate the electric potential energy of this system of charges by considering each pair of charges and summing up the contributions. The total potential energy is:

U = 1/2 [(3×2.4×10^-9)×(2×2.4×10^-9)/(4πε0×0.1) + (3×2.4×10^-9)×(2.4×10^-9)/(4πε0×0.2) + (2×2.4×10^-9)×(2.4×10^-9)/(4πε0×0.3) + (3×2.4×10^-9)×(2.4×10^-9)/(4πε0×0.3) + (2.4×10^-9)×(2.4×10^-9)/(4πε0×0.4) + (2.4×10^-9)×(2.4×10^-9)/(4πε0×0.5)]

Using the value of ε0 and simplifying, we get:

U = 4.1 × 10^-6 J

Therefore, the correct answer is A.

Consider the Group of Three+2